Simulation of Natural Convection with Sinusoidal Temperature Distribution of Heat Source at the Bottom of an Enclosed Square Cavity

The lattice Boltzmann method is employed in the current study to simulate the heat transfer characteristics of sinusoidal-temperature-distributed heat sources at the bottom of a square cavity under various conditions, including different amplitudes, phase angles, initial positions, and angular velocities. Additionally, a machine learning-based model is developed to accurately predict the Nusselt number in such a sinusoidal temperature distribution of heat source at the bottom of a square cavity. The results indicate that (1) in the phase angle range from 0 to π, Nu basically shows a decreasing trend with an increase in phase angle. The decline in Nu at an accelerated rate is consistently observed when the phase angle reaches 4π/16. The corresponding Nu decreases as the amplitude increases at the same phase angle. (2) The initial position of the sinusoidal-temperature-distributed heat source Lc significantly impacts the convective heat transfer in the cavity. Moreover, the decline in Nu was further exacerbated when Lc reached 7/16. (3) The optimal overall heat transfer effect was achieved when the angular velocity of the non-uniform heat source reached π. As the angular velocity increases, the local Nu in the square cavity exhibits a gradual and oscillatory decline. Notably, it is observed that Nu at odd multiples of π surpasses that at even multiples of π. Furthermore, the current work integrates LBM with machine learning, enabling the development of a precise and efficient prediction model for simulating Nu under specific operational conditions. This research provides valuable insights into the application of machine learning in the field of heat transfer.

An effective and robust lattice Boltzmann model guided by atlas for hippocampal subregions segmentation

BACKGROUND

Given the varying vulnerability of the rostral and caudal regions of the hippocampus to neuropathology in the Alzheimer's disease (AD) continuum, accurately assessing structural changes in these subregions is crucial for early AD detection. The development of reliable and robust automatic segmentation methods for hippocampal subregions (HS) is of utmost importance.

OBJECTIVE

Our aim is to propose and validate a HS segmentation model that is both training-free and highly generalizable. This method should exhibit comparable accuracy and efficiency to state-of-the-art techniques. The segmented HS can serve as a biomarker for studying the progression of AD.

METHODS

We utilized the functional magnetic resonance imaging of the Brain's Integrated Registration and Segmentation Tool (FIRST) to segment the entire hippocampus. By intersecting the segmentation results with the Brainnetome (BN) atlas, we obtained coarse segmentation of the four HS regions. This coarse segmentation was then employed as a shape prior term in the lattice Boltzmann (LB) model, as well as for initializing contours. Additionally, image gradients and local gray levels were integrated into the external force terms of the LB model to refine the coarse segmentation results. We assessed the segmentation accuracy of the model using the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and evaluated the potential of the segmentation results as AD biomarkers on both the ADNI and Xuanwu datasets.

RESULTS

The median Dice similarity coefficients (DSC) for the left caudal, right caudal, left rostral, and right rostral hippocampus were 0.87, 0.88, 0.88, and 0.89, respectively. The proportion of segmentation results with a DSC exceeding 0.8 was 77%, 78%, 77%, and 94% for the respective regions. In terms of volume, the correlation coefficients between the segmentation results of the four HS regions and the gold standard were 0.95, 0.93, 0.96, and 0.96, respectively. Regarding asymmetry, the correlation coefficient between the segmentation result's right caudal minus left caudal and the corresponding gold standard was 0.91, while for right rostral minus left rostral, it was 0.93. Over time, we observed a decline in the volumes of the four HS regions and the total hippocampal volume of mild cognitive impairment (MCI) converters. Analysis of inter-group differences revealed that, except for the right rostral region in the ADNI dataset, the p-values for the four HS regions in the normal controls (NC), MCI, and AD groups from both datasets were all below 0.05. The right caudal hippocampal volume demonstrated correlation coefficients of 0.47 and 0.43 with the mini-mental state examination (MMSE) and Montreal cognitive assessment (MoCA), respectively. Similarly, the left rostral hippocampal volume showed correlation coefficients of 0.50 and 0.58 with MMSE and MoCA, respectively.

CONCLUSIONS

Our framework allows for direct application to different brain magnetic resonance (MR) datasets without the need for training. It eliminates the requirement for complex image preprocessing steps while achieving segmentation accuracy comparable to deep learning (DL) methods even with small sample sizes. Compared to traditional active contour models (ACM) and atlas-based methods, our approach exhibits significant speed advantages. The segmented HS regions hold promise as potential biomarkers for studying the progression of AD.

Wetting and Spreading Behavior of Axisymmetric Compound Droplets on Curved Solid Walls Using Conservative Phase Field Lattice Boltzmann Method

Compound droplets have received increasing attention due to their applications in many several areas, including medicine and materials. Previous works mostly focused on compound droplets on planar surfaces and, as such, the effects of curved walls have not been studied thoroughly. In this paper, the influence of the properties of curved solid wall (including the shape, curvature, and contact angle) on the wetting behavior of compound droplets is explored. The axisymmetric lattice Boltzmann method, based on the conservative phase field formulation for ternary fluids, was used to numerically study the wetting and spreading of a compound droplet of the Janus type on various curved solid walls at large density ratios, focusing on whether the separation of compound droplets occurs. Several types of wall geometries were considered, including a planar wall, a concave wall with constant curvature, and a convex wall with fixed or variable curvature (specifically, a prolate or oblate spheroid). The effects of surface wettability, interfacial angles, and the density ratio (of droplet to ambient fluid) on the wetting process were also explored. In general, it was found that, under otherwise identical conditions, droplet separation tends to happen more likely on more hydrophilic walls, under larger interfacial angles (measured inside the droplet), and at larger density ratios. On convex walls, a larger radius of curvature of the surface near the droplet was found to be helpful to split the Janus droplet. On concave walls, as the radius of curvature increases from a small value, the possibility to observe droplet separation first increases and then decreases. Several phase diagrams on whether droplet separation occurs during the spreading process were produced for different kinds of walls to illustrate the influences of various factors.

Analysis of fibrocalcific aortic valve stenosis: computational pre-and-post TAVR haemodynamics behaviours

Fibro-calcific aortic valve (AV) diseases are characterized by calcium growth or accumulation of fibrosis in the AV tissues. Fibrocalcific aortic stenosis (FAS) rises specifically in females, like calcification-induced aortic stenosis (CAS), may eventually necessitate valve replacement. Fluid-structure-interaction (FSI) computational models for severe CAS and FAS patients were developed using lattice Boltzmann method and multi-scale finite elements (FE). Three parametric AV models were introduced: pathology-free of non-calcified tri-and-bicuspid AVs with healthy collagen fibre network (CFN), a FAS model incorporated a thickened CFN with embedded small calcification volumes, and a CAS model employs healthy CFN with embedded high calcification volumes. The results indicate that the interaction between calcium deposits, adjacent tissue and fibres crucially influences haemodynamics and structural reactions. A fourth model of transcatheter aortic valve replacement (TAVR) post-procedure outcomes was created to study both CAS and FAS. TAVR-CAS had a higher maximum contact pressure and lower anchoring area than TAVR-FAS, making it prone to aortic tissue damage and migration. Finally, although the TAVR-CAS offered a larger opening area, its paravalvular leakage was higher. This may be attributed to a similar thrombogenicity potential characterizing both models. The computational framework emphasizes the significance of mechanobiology in FAS and underscores the requirement for tissue modelling at multiple scales.

Micro Lubrication and Heat Transfer in Wedge-Shaped Channel Slider with Convex Surface Texture Based on Lattice Boltzmann Method

Hydrodynamic lubrication is widely used between two relatively moving objects, and the effect of fluid flow state and temperature distribution on lubrication performance in wedge-shaped gaps is a popular topic to study. In this paper, the incompressible double-distribution lattice Boltzmann method (LBM) is applied to study the effect of micro convex surface texture on micro lubrication and heat transfer in wedge-shaped channels. By comparing this model with the analytical solution of an infinitely wide wedge slider, the maximum pressure calculated by LBM is 0.1081 MPa, and the maximum pressure calculated by the Reynolds equation is 0.1079 MPa. The error of the maximum pressure is 1.11%, and the Reynolds equation result is slightly smaller. The reason is that the Reynolds equation ignores the influence of fluid inertia force on oil film pressure. The results indicate that the application of LBM can be used to study lubrication problems. Compared with the Reynolds equation, LBM can calculate the velocity field and pressure field in the film thickness direction, and can also observe precise flow field details such as vortices. Three micro convex texture shapes were established to study the effects of different convex textures on micro lubrication and oil film temperature distribution, and the velocity distribution, temperature distribution and oil film pressure along the oil film thickness direction were given. Under the same conditions, comparing the oil film pressure with and without surface texture, the results show that the maximum oil film pressure with surface texture 3 is increased by about 4.34% compared with that without surface texture. The slightly convex texture can increase the hydrodynamic lubrication effect and obtain greater load-bearing capacity, helping to reduce the possibility of contact friction. The results show that the convex surface texture can improve the hydrodynamic lubrication performance, increase the load carrying capacity and reduce the possibility of contact friction, and the convex surface texture can influence the temperature distribution of the oil film. At 3.6 mm in the slider length direction and 7.5 μm in the oil film thickness direction, the temperature of surface texture 1 is 402.64 K, the temperature of surface texture 2 is 403.31 K, and the temperature of surface texture 3 is 403.99 K. The presence of vortices is captured at a high convergence ratio.

3D Model of Carbon Diffusion during Diffusional Phase Transformations

The microstructure plays a crucial role in determining the properties of metallic materials, in terms of both their strength and functionality in various conditions. In the context of the formation of microstructure, phase transformations that occur in materials are highly significant. These are processes during which the structure of a material undergoes changes, most commonly as a result of variations in temperature, pressure, or chemical composition. The study of phase transformations is a broad and rapidly evolving research area that encompasses both experimental investigations and modeling studies. A foundational understanding of carbon diffusion and phase transformations in materials science is essential for comprehending the behavior of materials under different conditions. This understanding forms the basis for the development and optimization of materials with desired properties. The aim of this paper is to create a three-dimensional model for carbon diffusion in the context of modeling diffusional phase transformations occurring in carbon steels. The proposed model relies on the utilization of the LBM (Lattice Boltzmann Method) and CUDA architecture. The resultant carbon diffusion model is intricately linked with a microstructure evolution model grounded in FCA (Frontal Cellular Automata). This manuscript provides a concise overview of the LBM and the FCA method. It outlines the structure of the developed three-dimensional model for carbon diffusion, details its correlation with the microstructure evolution model, and presents the developed algorithm for simulating carbon diffusion. Demonstrative examples of simulation results, illustrating the growth of the emerging phase and affected by various model parameters within particular planes of the 3D calculation domain, are also presented.

Microchannel Gas Flow in the Multi-Flow Regime Based on the Lattice Boltzmann Method

In this work, a lattice Boltzmann method (LBM) for studying microchannel gas flow is developed in the multi-flow regime. In the LBM, by comparing previous studies' results on effective viscosity in multi-flow regimes, the values of the rarefaction factor applicable to multi-flow regions were determined, and the relationship between relaxation time and Kn number with the rarefaction factor is given. The Kn number is introduced into the second-order slip boundary condition together with the combined bounce-back/specular-reflection (CBBSR) scheme to capture the gas flow in the multi-flow regime. Sensitivity analysis of the dimensionless flow rate to adjustable parameters using the Taguchi method was carried out, and the values of adjustable parameters were determined based on the results of the sensitivity analysis. The results show that the dimensionless flow rate is more sensitive to j than h. Numerical simulations of Poiseuille flow and pulsating flow in a microchannel with second-order slip boundary conditions are carried out to validate the method. The results show that the velocity profile and dimensionless flow rate simulated by the present numerical simulation method in this work are found in the multi-flow regime, and the phenomenon of annular velocity profile in the microchannel is reflected in the phases.

Effects of Different Motion Parameters on the Interaction of Fish School Subsystems

For a long time, fish school swimming has attracted a great deal of attention in biological systems, as fish schools can have complex hydrodynamic effects on individuals. This work adopted a non-iterative, immersed boundary-lattice Boltzmann method (IB-LBM). A numerical simulation of two-dimensional three-degree-of-freedom self-propelled fish, in side-by-side, staggered, and triangle formations, was conducted by adjusting spacing and motion parameters. A comprehensive analysis of individual speed gains and energy efficiencies in these formations was carried out. Furthermore, an analysis of the hydrodynamic characteristics of fish schools was performed, using instantaneous vorticity profiles and pressure fields. Certain studies have shown that passive interactions between individuals cannot always bring hydrodynamic benefits. The swimming efficiency of side-by-side formations in the same phase gradually increases as the distance decreases, but it also brings certain burdens to individuals when the phases are different. This paper also shows that the roles of passive interactions, spacing, and deflections affect fish school subsystems differently. When the low-pressure areas created by a wake vortex act on one side of an individual's body, the tail-end fish are good at gaining hydrodynamic benefits from it. This effect is not universal, and the degree to which individuals benefit from changes in exercise parameters varies. This study provides a theoretical basis for bioinspired robots, as well as providing certain insights into the mechanism of collective biological movement.

Efficient Quality Diversity Optimization of 3D Buildings through 2D Pre-Optimization

Quality diversity algorithms can be used to efficiently create a diverse set of solutions to inform engineers' intuition. But quality diversity is not efficient in very expensive problems, needing hundreds of thousands of evaluations. Even with the assistance of surrogate models, quality diversity needs hundreds or even thousands of evaluations, which can make its use infeasible. In this study, we try to tackle this problem by using a pre-optimization strategy on a lower-dimensional optimization problem and then map the solutions to a higher-dimensional case. For a use case to design buildings that minimize wind nuisance, we show that we can predict flow features around 3D buildings from 2D flow features around building footprints. For a diverse set of building designs, by sampling the space of 2D footprints with a quality diversity algorithm, a predictive model can be trained that is more accurate than when trained on a set of footprints that were selected with a space-filling algorithm like the Sobol sequence. Simulating only 16 buildings in 3D, a set of 1,024 building designs with low predicted wind nuisance is created. We show that we can produce better machine learning models by producing training data with quality diversity instead of using common sampling techniques. The method can bootstrap generative design in a computationally expensive 3D domain and allow engineers to sweep the design space, understanding wind nuisance in early design phases.

Perfusion of MC3T3E1 Preosteoblast Spheroids within Polysaccharide-Based Hydrogel Scaffolds: An Experimental and Numerical Study at the Bioreactor Scale

The traditional 3D culture systems in vitro lack the biological and mechanical spatiotemporal stimuli characteristic to native tissue development. In our study, we combined porous polysaccharide-based hydrogel scaffolds with a bioreactor-type perfusion device that generates favorable mechanical stresses while enhancing nutrient transfers. MC3T3E1 mouse osteoblasts were seeded in the scaffolds and cultivated for 3 weeks under dynamic conditions at a perfusion rate of 10 mL min^-1. The spatial distribution of the cells labeled with superparamagnetic iron oxide nanoparticles was visualized by MRI. Confocal microscopy was used to assess cell numbers, their distribution inside the scaffolds, cell viability, and proliferation. The oxygen diffusion coefficient in the hydrogel was measured experimentally. Numerical simulations of the flow and oxygen transport within the bioreactor were performed using a lattice Boltzmann method with a two-relaxation time scheme. Last, the influence of cell density and spheroid size on cell oxygenation was investigated. The cells spontaneously organized into spheroids with a diameter of 30-100 μm. Cell viability remained unchanged under dynamic conditions but decreased under static culture. The cell proliferation (Ki67 expression) in spheroids was not observed. The flow simulation showed that the local fluid velocity reached 27 mm s^-1 at the height where the cross-sectional area of the flow was the smallest. The shear stress exerted by the fluid on the scaffolds may locally rise to 100 mPa, compared with the average value of 25 mPa. The oxygen diffusion coefficient in the hydrogel was 1.6×10-9 m² s^-1. The simulation of oxygen transport and consumption confirmed that the cells in spheroids did not suffer from hypoxia when the bioreactor was perfused at 10 mL min^-1, and suggested the existence of optimal spheroid size and spacing for appropriate oxygenation. Collectively, these findings enabled us to define the optimal conditions inside the bioreactor for an efficient in vitro cell organization and survival in spheroids, which are paramount to future applications with organoids.

3D Model of Heat Flow during Diffusional Phase Transformations

The structure of metallic materials has a significant impact on their properties. One of the most popular methods to form the properties of metal alloys is heat treatment, which uses thermally activated transformations that take place in metals to achieve the required mechanical or physicochemical properties. The phase transformation in steel results from the fact that one state becomes less durable than the other due to a change in conditions, for example, temperature. Phase transformations are an extensive field of research that is developing very dynamically both in the sphere of experimental and model research. The objective of this paper is the development of a 3D heat flow model to model heat transfer during diffusional phase transformations in carbon steels. This model considers the two main factors that influence the transformation: the temperature and the enthalpy of transformation. The proposed model is based on the lattice Boltzmann method (LBM) and uses CUDA parallel computations. The developed heat flow model is directly related to the microstructure evolution model, which is based on frontal cellular automata (FCA). This paper briefly presents information on the FCA, LBM, CUDA, and diffusional phase transformation in carbon steels. The structures of the 3D model of heat flow and their connection with the microstructure evolution model as well as the algorithm for simulation of heat transfer with consideration of the enthalpy of transformation are shown. Examples of simulation results of the growth of the new phase that are determined by the overheating/overcooling and different model parameters in the selected planes of the 3D calculation domain are also presented.

Pore-Scale Modeling of Liquid Water Transport in Compressed Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells Considering Fiber Anisotropy

Water management of the gas diffusion layer (GDL) is crucial to the performance of proton exchange membrane fuel cells (PEMFCs). Appropriate water management ensures efficient transport of reactive gases and maintains wetting of the proton exchange membrane to enhance proton conduction. In this paper, a two-dimensional pseudo-potential multiphase lattice Boltzmann model is developed to study liquid water transport within the GDL. Liquid water transport from the GDL to the gas channel is the focus, and the effect of fiber anisotropy and compression on water management is evaluated. The results show that the fiber distribution approximately perpendicular to the rib reduces liquid water saturation within the GDL. Compression significantly changes the microstructure of the GDL under the ribs, which facilitates the formation of liquid water transport pathways under the gas channel, and the increase in the compression ratio leads to a decrease in liquid water saturation. The performed microstructure analysis and the pore-scale two-phase behavior simulation study comprise a promising technique for optimizing liquid water transport within the GDL.

An Explicit-Correction-Force Scheme of IB-LBM Based on Interpolated Particle Distribution Function

In order to obtain a better numerical simulation method for fluid-structure interaction (FSI), the IB-LBM combining the lattice Boltzmann method (LBM) and immersed boundary method (IBM) has been studied more than a decade. For this purpose, an explicit correction force scheme of IB-LBM was proposed in this paper. Different from the current IB-LBMs, this paper introduced the particle distribution function to the interpolation process from the fluid grids to the immersed boundary at the mesoscopic level and directly applied the LBM force models to obtain the interface force with a simple form and explicit process. Then, in order to ensure the mass conservation in the local area of the interface, this paper corrected the obtained interface force with the correction matrix, forming the total explicit-correction-force (ECP) scheme of IB-LBM. The results of four numerical tests were used to verify the order of accuracy and effectiveness of the present method. The streamline penetration is limited and the numerical simulation with certain application significance is successful for complex boundary conditions such as the movable rigid bodies (free oscillation of the flapping foil) and flexible deformable bodies (free deformation of cylinders). In summary, we obtained a simple and alternative simulation method that can achieve good simulation results for engineering reference models with complex boundary problems.

Effects of Compression and Porosity Gradients on Two-Phase Behavior in Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells

Water management within the gas diffusion layer (GDL) plays an important role in the performance of the proton exchange membrane fuel cell (PEMFC) and its reliability. The compression of the gas diffusion layer during fabrication and assembly has a significant impact on the mass transport, and the porosity gradient design of the gas diffusion layer is an essential way to improve water management. In this paper, the two-dimensional lattice Boltzmann method (LBM) is applied to investigate the two-phase behavior in gas diffusion layers with different porosity gradients under compression. Compression results in an increase in flow resistance below the ribs, prompting the appearance of the flow path of liquid water below the channel, and liquid water breaks through to the channel more quickly. GDLs with linear, multilayer, and inverted V-shaped porosity distributions with an overall porosity of 0.78 are generated to evaluate the effect of porosity gradients on the liquid water transport. The liquid water saturation values within the linear and multilayer GDLs are significantly reduced compared to that of the GDL with uniform porosity, but the liquid water within the inverted V-shaped GDL accumulates in the middle region and is more likely to cause flooding.

Mechanistic Insight into Wettability Enhancement of Lithium-Ion Batteries Using a Ceramic-Coated Layer

The crucial issue of wettability in high-energy-density lithium-ion batteries (LIBs) has not been comprehensively addressed to date. To overcome the challenge, state-of-the-art LIBs employing a ceramic-coated separator improves the safety- and wettability-related aspects of LIBs. Here, we present a mechanistic study of the effects of a ceramic-coated layer (CCL) on electrode wettability and report the optimal position of the CCL in LIBs. The electrolyte wetting was investigated using the multiphase lattice Boltzmann method and electrochemical impedance spectroscopy for capturing the electrolyte-transport dynamics in porous electrodes and impedance spectra in pouch-type LIBs, respectively. Results indicate that the CCL caused the velocity vector to transport the electrolyte further, resulting in an increase in the wetting rate. Moreover, the location of the CCL considerably affected the wettability of the LIBs. This study provides mechanical insight into the design and fabrication of high-performance LIBs by incorporating CCLs.

Numerical Study on Heat-Transfer Characteristics of Convection Melting in Metal Foam under Sinusoidal Temperature Boundary Conditions

Convection melting in metal foam under sinusoidal temperature boundary conditions is numerically studied in the present study. A multiple-relaxation-time lattice Boltzmann method, in conjunction with the enthalpy approach, is constructed to model the melting process without iteration steps. The effects of the porosity, phase deviation, and periodicity parameter on the heat-transfer characteristics are investigated. For the cases considered in this work, it is found that the effects of the phase deviation and periodicity parameter on the melting rate are weak, but the melting front can be significantly affected by the sinusoidal temperature boundary conditions.

Movable and Focus-Tunable Lens Based on Electrically Controllable Liquid: A Lattice Boltzmann Study

Adjusting the focal length by changing the liquid interface of the liquid lens has become a potential method. In this paper, the lattice-Boltzmann-electrodynamic (LB-ED) method is used to numerically investigate the zooming process of a movable and focus-tunable electrowetting-on-dielectrics (EWOD) liquid lens by combining the LBM chemical potential model and the electrodynamic model. The LB method is used to solve the Navier-Stokes equation, and the Poisson-Boltzmann (PB) equation is introduced to solve the electric field distribution. The experimental results are consistent with the theoretical results of the Lippmann-Young equation. Through the simulation of a liquid lens zoom driven by EWOD, it is found that the lens changes from a convex lens to a concave lens with the voltage increases. The focal length change rate in the convex lens stage gradually increases with voltage. In the concave lens stage, the focal length change rate is opposite to that in the convex lens stage. During the zooming process, the low-viscosity liquid exhibits oscillation, and the high-viscosity liquid appears as overdamping. Additionally, methods were proposed to accelerate lens stabilization at low and high viscosities, achieving speed improvements of about 30% and 50%, respectively. Simulations of lens motion at different viscosities demonstrate that higher-viscosity liquids require higher voltages to achieve the same movement speed.

Pore-Level Multiphase Simulations of Realistic Distillation Membranes for Water Desalination

Membrane distillation (MD) is a thermally driven separation process that is operated below boiling point. Since the performance of MD modules is still comparatively low, current research aims to improve the understanding of the membrane structure and its underlying mechanisms at the pore level. Based on existing realistic 3D membrane geometries (up to 0.5 billion voxels with 39nm resolution) obtained from ptychographic X-ray computed tomography, the D3Q27 lattice Boltzmann (LB) method was used to investigate the interaction of the liquid and gaseous phase with the porous membrane material. In particular, the Shan and Chen multi-phase model was used to simulate multi-phase flow at the pore level. We investigated the liquid entry pressure of different membrane samples and analysed the influence of different micropillar structures on the Wenzel and Cassie-Baxter state of water droplets on rough hydrophobic surfaces. Moreover, we calculated the liquid entry pressure required for entering the membrane pores and extracted realistic water contact surfaces for different membrane samples. The influence of the micropillars and flow on the water-membrane contact surface was investigated. Finally, we determined the air-water interface within a partially saturated membrane, finding that the droplet size and distribution correlated with the porosity of the membrane.

New Platforms Based on Frontal Cellular Automata and Lattice Boltzmann Method for Modeling the Forming and Additive Manufacturing

Materials science gives theoretical and practical tools, while new modeling methods and platforms provide rapid and efficient development, improvement, and optimization of old and new technologies. Recently, impressive progress has been made in the development of computer software and systems. The frontal cellular automata (FCA), lattice Boltzmann method (LBM), and modeling platforms based on them are considered in the paper. The paper presents basic information on these methods and their application for modeling phenomena and processes in materials science. Recrystallization, crystallization, phase transformation, processes such as flat and shape rolling, additive manufacturing technologies (Selective Laser Sintering (SLS)/ Selective Laser Melting (SLM)), and others are examples of comprehensive and effective modeling by the developed systems. Selected modeling results are also presented.

Swimming Mode of Two Interacting Squirmers under Gravity in a Narrow Vertical Channel

The swimming mode of two interacting squirmers under gravity in a narrow vertical channel is simulated numerically using the lattice Boltzmann method (LBM) in the range of self-propelling strength 0.1 ≤ α ≤ 1.1 and swimming type −5 ≤ β ≤ 5. The results showed that there exist five typical swimming patterns for individual squirmers, i.e., steady upward rising (SUR), oscillation across the channel (OAC), oscillation near the wall (ONW), steady upward rising with small-amplitude oscillation (SURO), and vertical motion along the sidewall (VMS). The parametric space (α, β) illustrated the interactions on each pattern. In particular, the range of oscillation angle for ONW is from 19.8° to 32.4° as α varies from 0.3 to 0.7. Moreover, the swimming modes of two interacting squirmers combine the two squirmers’ independent swimming patterns. On the other hand, the pullers (β < 0) attract with each other at the initial stage, resulting in a low-pressure region between them and making the two pullers gradually move closer and finally make contact, while the result for the pushers (β > 0) is the opposite. After the squirmers’ interaction, the squirmer orientation and pressure distribution determine subsequent squirmer swimming patterns. Two pushers separate quickly, while there will be a more extended interaction period before the two pullers are entirely separated.

Effect of cilia-induced surface velocity on cerebrospinal fluid exchange in the lateral ventricles

Ciliary motility disorders are known to cause hydrocephalus. The instantaneous velocity of cerebrospinal fluid (CSF) flow is dominated by artery pulsation, and it remains unclear why ciliary dysfunction results in hydrocephalus. In this study, we investigated the effects of cilia-induced surface velocity on CSF flow using computational fluid dynamics. A geometric model of the human ventricles was constructed using medical imaging data. The CSF produced by the choroid plexus and cilia-induced surface velocity were given as the velocity boundary conditions at the ventricular walls. We developed healthy and reduced cilia motility models based on experimental data of cilia-induced velocity in healthy wild-type and Dpcd-knockout mice. The results indicate that there is almost no difference in intraventricular pressure between healthy and reduced cilia motility models. Additionally, it was found that newly produced CSF from the choroid plexus did not spread to the anterior and inferior horns of the lateral ventricles in the reduced cilia motility model. These findings suggest that a ciliary motility disorder could delay CSF exchange in the anterior and inferior horns of the lateral ventricles.

Endothelial glycocalyx permeability for nanoscale solutes

Glycocalyx has a great impact on the accessibility of the endothelial cell membranes. Although the specific interactions play a crucial role in cross-membrane solute transport, nonspecific interactions cannot be neglected. In this work, we used computational modeling to quantify the nonspecific interactions that control the distribution of nanosized solutes across the endothelial glycocalyx. We evaluated the probabilities of various nanoparticles' passage through the luminal layer to the membrane. The calculations demonstrate that excluded volume and electrostatic interactions are decisive for the solute transport as compared with van der Waals and hydrodynamic interactions. Damaged glycocalyx models showed a relatively weak efficiency in sieving plasma solutes. We estimated the energy barriers and corresponding mean first passage times for nanoscale solute transport through the model glycocalyx.

Numerical investigation of the formation and stability of homogeneous pairs of soft particles in inertial microfluidics

We investigate the formation and stability of a pair of identical soft capsules in channel flow under mild inertia. We employ a combination of the lattice Boltzmann, finite element and immersed boundary methods to simulate the elastic particles in flow. Validation tests show excellent agreement with numerical results obtained by other research groups. Our results reveal new trajectory types that have not been observed for pairs of rigid particles. While particle softness increases the likelihood of a stable pair forming, the pair stability is determined by the lateral position of the particles. A key finding is that stabilisation of the axial distance occurs after lateral migration of the particles. During the later phase of pair formation, particles undergo damped oscillations that are independent of initial conditions. These damped oscillations are driven by a strong hydrodynamic coupling of the particle dynamics, particle inertia and viscous dissipation. While the frequency and damping coefficient of the oscillations depend on particle softness, the pair formation time is largely determined by the initial particle positions: the time to form a stable pair grows exponentially with the initial axial distance. Our results demonstrate that particle softness has a strong impact on the behaviour of particle pairs. The findings could have significant ramifications for microfluidic applications where a constant and reliable axial distance between particles is required, such as flow cytometry.

Dynamics of two-dimensional liquid bridges

We have simulated the motion of a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates of given wettabilities, using a multicomponent pseudopotential lattice Boltzmann method. For this simple geometry, the Young-Laplace equation can be solved (quasi-)analytically to yield the equilibrium bridge shape under gravity, which provides a check on the validity of the numerical method. In steady-state conditions, we calculate the drag force exerted by the moving bridge on the confining substrates as a function of its velocity, for different contact angles and Bond numbers. We also study how the bridge deforms as it moves, as parametrized by the changes in the advancing and receding contact angles at the substrates relative to their equilibrium values. Finally, starting from a bridge within the range of contact angles and Bond numbers in which it can exist at equilibrium, we investigate how fast it must move in order to break up.

Molecular dynamics lattice gas equilibrium distribution function for Lennard-Jones particles

The molecular dynamics lattice gas (MDLG) method maps a molecular dynamics (MD) simulation onto a lattice gas using a coarse-graining procedure. This is a novel fundamental approach to derive the lattice Boltzmann method (LBM) by taking a Boltzmann average over the MDLG. A key property of the LBM is the equilibrium distribution function, which was originally derived by assuming that the particle displacements in the MD simulation are Boltzmann distributed. However, we recently discovered that a single Gaussian distribution function is not sufficient to describe the particle displacements in a broad transition regime between free particles and particles undergoing many collisions in one time step. In a recent publication, we proposed a Poisson weighted sum of Gaussians which shows better agreement with the MD data. We derive a lattice Boltzmann equilibrium distribution function from the Poisson weighted sum of Gaussians model and compare it to a measured equilibrium distribution function from MD data and to an analytical approximation of the equilibrium distribution function from a single Gaussian probability distribution function. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Lattice Boltzmann simulations on the tumbling to tank-treading transition: effects of membrane viscosity

The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio [Formula: see text] (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate [Formula: see text] applied to the RBC. However, the membrane viscosity [Formula: see text] plays a major role in a realistic description of RBC dynamics, and only a few works have systematically focused on its effects on the TB-TT transition. In this work, we provide a parametric investigation on the effect of membrane viscosity [Formula: see text] on the TB-TT transition for a single RBC. It is found that, at fixed viscosity ratios [Formula: see text], larger values of [Formula: see text] lead to an increased range of values of capillary number at which the TB-TT transition occurs; moreover, we found that increasing [Formula: see text] or increasing [Formula: see text] results in a qualitatively but not quantitatively similar behaviour. All results are obtained by means of mesoscale numerical simulations based on the lattice Boltzmann models. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh-Taylor system

We develop a multicomponent lattice Boltzmann (LB) model for the two-dimensional Rayleigh-Taylor turbulence with a Shan-Chen pseudopotential implemented on GPUs. In the immiscible case, this method is able to accurately overcome the inherent numerical complexity caused by the complicated structure of the interface that appears in the fully developed turbulent regime. The accuracy of the LB model is tested both for early and late stages of instability. For the developed turbulent motion, we analyse the balance between different terms describing variations of the kinetic and potential energies. Then we analyse the role of the interface in the energy balance and also the effects of the vorticity induced by the interface in the energy dissipation. Statistical properties are compared for miscible and immiscible flows. Our results can also be considered as a first validation step to extend the application of LB model to three-dimensional immiscible Rayleigh-Taylor turbulence. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Neutrally Buoyant Particle Migration in Poiseuille Flow Driven by Pulsatile Velocity

A neutrally buoyant circular particle migration in two-dimensional (2D) Poiseuille channel flow driven by pulsatile velocity is numerical studied by using immersed boundary-lattice Boltzmann method (IB-LBM). The effects of Reynolds number (25≤Re≤200) and blockage ratio (0.15≤k≤0.40) on particle migration driven by pulsatile and non-pulsatile velocity are all numerically investigated for comparison. The results show that, different from non-pulsatile cases, the particle will migrate back to channel centerline with underdamped oscillation during the time period with zero-velocity in pulsatile cases. The maximum lateral travel distance of the particle in one cycle of periodic motion will increase with increasing Re, while k has little impact. The quasi frequency of such oscillation has almost no business with Re and k. Moreover, Re plays an essential role in the damping ratio. Pulsatile flow field is ubiquitous in aorta and other arteries. This article is conducive to understanding nanoparticle migration in those arteries.

Lattice Boltzmann simulation of transient blood flow in arterial geometries using a regularised, viscoplastic and shear-thinning fluid

This paper presents a lattice Boltzmann framework for the transient simulation of blood flow using biologically inspired geometries and pressure boundary conditions. The Kuang-Luo rheological model is used to represent blood as a homogeneous continuum. This model includes the two primary non-Newtonian characteristics of blood, namely viscoplasticity and pseudoplasticity. This paper makes two contributions. First, the numerical challenges associated with zero strain rates and infinite viscosity, as a consequence of the yield stress in the Kuang-Luo model, were addressed by regularising the constitutive equation so that the viscosity tends towards a finite value at low strain rates. A two-relaxation-time operator, which exhibits improved performance over the single-relaxation-time operator and lower computational overhead than the multiple-relaxation-time operator, is employed in the collision process. The recursive relationship between the local strain rate and relaxation rate was addressed by use of an implicit solver for these two quantities. The implemented model was benchmarked against analytic solutions for Poiseuille flow between parallel plates in two dimensions and in a cylindrical tube in three dimensions. More importantly, the transient performance of the implemented model was demonstrated by matching the predicted start-up flow of the Poiseuille flow of a Bingham fluid with the corresponding analytical solution. Second, the numerical developments were applied in the simulation of transient blood flow in complex configurations. The development and implementation of physically inspired pressure profiles highlighted the shortcomings of using a sinusoidal pressure profile in the prediction of velocity and stress distributions. Finally, the simulation of blood flow in a section of a carotid artery indicated a number of flow characteristics that will be of interest to future investigations of clinical problems.

A Parallel Coupled Lattice Boltzmann-Volume of Fluid Framework for Modeling Porous Media Evolution

In this paper, we present a framework for the modeling and simulation of a subset of physical/chemical processes occurring on different spatial and temporal scales in porous materials. In order to improve our understanding of such processes on multiple spatio-temporal scales, small-scale simulations of transport and reaction are of vital importance. Due to the geometric complexity of the pore space and the need to consider a representative elementary volume, such simulations require substantial numerical resolutions, leading to potentially huge computation times. An efficient parallelization of such numerical methods is thus vital to obtain results in acceptable wall-clock time. The goal of this paper was to improve available approaches based on lattice Boltzmann methods (LBMs) to reliably and accurately predict the combined effects of mass transport and reaction in porous media. To this end, we relied on the factorized central moment LBM as a second-order accurate approach for modeling transport. In order to include morphological changes due to the dissolution of the solid phase, the volume of fluid method with the piece-wise linear interface construction algorithm was employed. These developments are being integrated into the LBM research code VirtualFluids. After the validation of the analytic test cases, we present an application of diffusion-controlled dissolution for a pore space obtained from computer tomography (CT) scans.

Extended Lattice Boltzmann Model

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.

Towards blood flow in the virtual human: efficient self-coupling of HemeLB

Many scientific and medical researchers are working towards the creation of a virtual human—a personalized digital copy of an individual—that will assist in a patient’s diagnosis, treatment and recovery. The complex nature of living systems means that the development of this remains a major challenge. We describe progress in enabling the HemeLB lattice Boltzmann code to simulate 3D macroscopic blood flow on a full human scale. Significant developments in memory management and load balancing allow near linear scaling performance of the code on hundreds of thousands of computer cores. Integral to the construction of a virtual human, we also outline the implementation of a self-coupling strategy for HemeLB. This allows simultaneous simulation of arterial and venous vascular trees based on human-specific geometries.

Effective Diffusion in Fibrous Porous Media: A Comparison Study between Lattice Boltzmann and Pore Network Modeling Methods

The understanding of the correlation between a pore-scale structure and its coupled diffusion transport property is crucial in the virtual design and performance optimization of porous fibrous material for various energy applications. Two most common and widely employed pore-scale modeling techniques are the lattice Boltzmann method (LBM) and the pore network modeling (PNM). However, little attention has been paid to the direct comparison between these two methods. To this end, stochastic porous fibrous structures are reconstructed reflecting the structural properties of the fibrous porous material on a statistical level with structural properties obtained from X-ray computed microtomography. Diffusion simulation through the porous phase was subsequently conducted using LBM of D3Q7 lattice and topological equivalent PNM derived from the watershed method, respectively. It is detected that the effective diffusion coefficients between these two methods are in good agreement when the throat radius in the pore network is estimated using the cross-section area equivalent radius. Like most literature, the diffusivity in the in-plane (IP) direction is larger than in the through-plane (TP) direction due to the laid fiber arrangement, but the values are very close. Besides, tortuosity was evaluated from both geometry and transport measurements. Tortuosity values deduced from both methods are in line with the anisotropy of the diffusion coefficients.

Lattice Boltzmann Solver for Multiphase Flows: Application to High Weber and Reynolds Numbers

The lattice Boltzmann method, now widely used for a variety of applications, has also been extended to model multiphase flows through different formulations. While already applied to many different configurations in low Weber and Reynolds number regimes, applications to higher Weber/Reynolds numbers or larger density/viscosity ratios are still the topic of active research. In this study, through a combination of a decoupled phase-field formulation—the conservative Allen–Cahn equation—and a cumulant-based collision operator for a low-Mach pressure-based flow solver, we present an algorithm that can be used for higher Reynolds/Weber numbers. The algorithm was validated through a variety of test cases, starting with the Rayleigh–Taylor instability in both 2D and 3D, followed by the impact of a droplet on a liquid sheet. In all simulations, the solver correctly captured the flow dynamics andmatched reference results very well. As the final test case, the solver was used to model droplet splashing on a thin liquid sheet in 3D with a density ratio of 1000 and kinematic viscosity ratio of 15, matching the water/air system at We = 8000 and Re = 1000. Results showed that the solver correctly captured the fingering instabilities at the crown rim and their subsequent breakup, in agreement with experimental and numerical observations reported in the literature.

A Novel Multiscale Methodology for Simulating Droplet Morphology Evolution during Injection Molding of Polymer Blends

The morphology of polymer blends plays a critical role in determining the properties of the blends and performance of resulting injection-molded parts. However, it is currently impossible to predict the morphology evolution during injection molding and the final micro-structure of the molded parts, as the existing models for the morphology evolution of polymer blends are still limited to a few simple flow fields. To fill this gap, this paper proposed a novel model for droplet morphology evolution during the mold filling process of polymer blends by coupling the models on macro- and meso-scales. The proposed model was verified by the injection molding experiment of PP/POE blends. The predicted curve of mold cavity pressure during filling process agreed precisely with the data of the corresponding pressure sensors. On the other hand, the model successfully tracked the moving trajectory and simulated morphology evolution of the droplets during the mold-filling process. After mold-filling ended, the simulation results of the final morphology of the droplets were consistent with the observations of the scanning electron microscope (SEM) experiment. Moreover, this study revealed the underlying mechanism of the droplet morphology evolution through the force analysis on the droplet. It is validated that the present model is a qualified tool for simulating the morphology evolution of polymer blends during injection molding and predicting the final microstructure of the products.

A fully coupled hybrid lattice Boltzmann and finite difference method-based study of transient electrokinetic flows

Transient electrokinetic (EK) flows involve the transport of conductivity gradients developed as a result of mixing of ionic species in the fluid, which in turn is affected by the electric field applied across the channel. The presence of three different coupled equations with corresponding different time scales makes it difficult to model the problem using the lattice Boltzmann method (LBM). The present work aims to develop a hybrid LBM and finite difference method (FDM)-based model which can be used to study the electro-osmotic flows (EOFs) and the onset of EK instabilities using an Ohmic model, where fluid and conductivity transport are solved using LBM and the electric field is solved using FDM. The model developed will be used to simulate three different problems: (i) EOF with varying zeta-potential on the wall, (ii) similitude in EOF, and (iii) EK instabilities due to the presence of conductivity gradients. Problems (i) and (ii) will be compared with the analytical results and problem (iii) will be compared with the simulations of a spectral method-based numerical model. The results obtained from the present simulations will show that the developed model is capable of studying transient EK flows and of predicting the onset of instability.

Three-Dimensional Numerical Simulation of Particle Focusing and Separation in Viscoelastic Fluids

Particle focusing and separation using viscoelastic microfluidic technology have attracted lots of attention in many applications. In this paper, a three-dimensional lattice Boltzmann method (LBM) coupled with the immersed boundary method (IBM) is employed to study the focusing and separation of particles in viscoelastic fluid. In this method, the viscoelastic fluid is simulated by the LBM with two sets of distribution functions and the fluid-particle interaction is calculated by the IBM. The performance of particle focusing under different microchannel aspect ratios (AR) is explored and the focusing equilibrium positions of the particles with various elasticity numbers and particle diameters are compared to illustrate the mechanism of particle focusing and separation in viscoelastic fluids. The results indicate that, for particle focusing in the square channel (AR = 1), the centerline single focusing becomes a bistable focusing at the centerline and corners as El increases. In the rectangular channels (AR < 1), particles with different diameters have different equilibrium positions. The equilibrium position of large particles is closer to the wall, and large particles have a faster lateral migration speed and few large particles migrate towards the channel center. Compared with the square channel, the rectangular channel is a better design for particle separation.

Reviving the local second-order boundary approach within the two-relaxation-time lattice Boltzmann modelling

This work addresses the Dirichlet boundary condition for momentum in the lattice Boltzmann method (LBM), with focus on the steady-state Stokes flow modelling inside non-trivial shaped ducts. For this task, we revisit a local and highly accurate boundary scheme, called the local second-order boundary (LSOB) method. This work reformulates the LSOB within the two-relaxation-time (TRT) framework, which achieves a more standardized and easy to use algorithm due to the pivotal parametrization TRT properties. The LSOB explicitly reconstructs the unknown boundary populations in the form of a Chapman-Enskog expansion, where not only first- but also second-order momentum derivatives are locally extracted with the TRT symmetry argument, through a simple local linear algebra procedure, with no need to compute their non-local finite-difference approximations. Here, two LSOB strategies are considered to realize the wall boundary condition, the original one called Lwall and a novel one Lnode, which operate with the wall and node variables, roughly speaking. These two approaches are worked out for both plane and curved walls, including the corners. Their performance is assessed against well-established LBM boundary schemes such as the bounce-back, the local second-order accurate CLI scheme and two different parabolic multi-reflection (MR) schemes. They are all evaluated for 3D duct flows with rectangular, triangular, circular and annular cross-sections, mimicking the geometrical challenges of real porous structures. Numerical tests confirm that LSOB competes with the parabolic MR accuracy in this problem class, requiring only a single node to operate. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Efficient supersonic flow simulations using lattice Boltzmann methods based on numerical equilibria

A double-distribution-function based lattice Boltzmann method (DDF-LBM) is proposed for the simulation of polyatomic gases in the supersonic regime. The model relies on a numerical equilibrium that has been extensively used by discrete velocity methods since the late 1990s. Here, it is extended to reproduce an arbitrary number of moments of the Maxwell-Boltzmann distribution. These extensions to the standard 5-constraint (mass, momentum and energy) approach lead to the correct simulation of thermal, compressible flows with only 39 discrete velocities in 3D. The stability of this BGK-LBM is reinforced by relying on Knudsen-number-dependent relaxation times that are computed analytically. Hence, high Reynolds-number, supersonic flows can be simulated in an efficient and elegant manner. While the 1D Riemann problem shows the ability of the proposed approach to handle discontinuities in the zero-viscosity limit, the simulation of the supersonic flow past a NACA0012 aerofoil confirms the excellent behaviour of this model in a low-viscosity and supersonic regime. The flow past a sphere is further simulated to investigate the 3D behaviour of our model in the low-viscosity supersonic regime. The proposed model is shown to be substantially more efficient than the previous 5-moment D3Q343 DDF-LBM for both CPU and GPU architectures. It then opens up a whole new world of compressible flow applications that can be realistically tackled with a purely LB approach. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Impact of collision models on the physical properties and the stability of lattice Boltzmann methods

The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two kinds of solutions were proposed in the literature. They consist in changing either the numerical discretization (finite-volume, finite-difference, spectral-element, etc.) of the discrete velocity Boltzmann equation (DVBE), or the collision model. In this work, the latter solution is investigated in detail. More precisely, we propose a comprehensive comparison of (static relaxation time based) collision models, in terms of stability, and with preliminary results on their accuracy, for the simulation of isothermal high-Reynolds number flows in the (weakly) compressible regime. It starts by investigating the possible impact of collision models on the macroscopic behaviour of stream-and-collide based D2Q9-LBMs, which clarifies the exact physical properties of collision models on LBMs. It is followed by extensive linear and numerical stability analyses, supplemented with an accuracy study based on the transport of vortical structures over long distances. In order to draw conclusions as generally as possible, the most common moment spaces (raw, central, Hermite, central Hermite and cumulant), as well as regularized approaches, are considered for the comparative studies. LBMs based on dynamic collision mechanisms (entropic collision, subgrid-scale models, explicit filtering, etc.) are also briefly discussed. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

A multi-component lattice Boltzmann approach to study the causality of plastic events

Using a multi-component lattice Boltzmann (LB) model, we perform fluid kinetic simulations of confined and concentrated emulsions. The system presents the phenomenology of soft-glassy materials, including a Herschel-Bulkley rheology, yield stress, ageing and long relaxation time scales. Shearing the emulsion in a Couette cell below the yield stress results in plastic topological re-arrangement events which follow established empirical seismic statistical scaling laws, making this system a good candidate to study the physics of earthquakes. One characteristic of this model is the tendency for events to occur in avalanche clusters, with larger events, triggering subsequent re-arrangements. While seismologists have developed statistical tools to study correlations between events, a process to confirm causality remains elusive. We present here, a modification to our LB model, involving small, fast vibrations applied to individual droplets, effectively a macroscopic forcing, which results in the arrest of the topological plastic re-arrangements. This technique provides an excellent tool for identifying causality in plastic event clusters by examining the evolution of the dynamics after 'stopping' an event, and then checking which subsequent events disappear. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Plasma-induced catalysis: towards a numerical approach

A lattice Boltzmann (LB) model is developed, validated and used to study simplified plasma/flow problems in complex geometries. This approach solves a combined set of equations, namely the Navier-Stokes equations for the momentum field, the advection-diffusion and the Nernst-Planck equations for electrokinetic and the Poisson equation for the electric field. This model allows us to study the dynamical interaction of the fluid/plasma density, velocity, concentration and electric field. In this work, we discuss several test cases for our numerical model and use it to study a simplified plasma fluid flowing and reacting inside a packed bed reactor. Inside the packed bed, electric breakdown reactions take place due to the electric field, making neutral species ionize. The presence of the packed beads can help enhance the reaction efficiency by locally increasing the electric field, and the size of packed beads and the pressure drop of the packed bed do influence the outflux. Hence trade-offs exist between reaction efficiency and packing porosity, the size of packing beads and the pressure drop of the packed bed. Our model may be used as a guidance to achieve higher reaction efficiencies by optimizing the relevant parameters. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Compressibility in lattice Boltzmann on standard stencils: effects of deviation from reference temperature

With growing interest in the simulation of compressible flows using the lattice Boltzmann (LB) method, a number of different approaches have been developed. These methods can be classified as pertaining to one of two major categories: (i) solvers relying on high-order stencils recovering the Navier-Stokes-Fourier equations, and (ii) approaches relying on classical first-neighbour stencils for the compressible Navier-Stokes equations coupled to an additional (LB-based or classical) solver for the energy balance equation. In most cases, the latter relies on a thermal Hermite expansion of the continuous equilibrium distribution function (EDF) to allow for compressibility. Even though recovering the correct equation of state at the Euler level, it has been observed that deviations of local flow temperature from the reference can result in instabilities and/or over-dissipation. The aim of the present study is to evaluate the stability domain of different EDFs, different collision models, with and without the correction terms for the third-order moments. The study is first based on a linear von Neumann analysis. The correction term for the space- and time-discretized equations is derived via a Chapman-Enskog analysis and further corroborated through spectral dispersion-dissipation curves. Finally, a number of numerical simulations are performed to illustrate the proposed theoretical study. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Multi-GPU Immersed Boundary Method Hemodynamics Simulations

Large-scale simulations of blood flow that resolve the 3D deformation of each comprising cell are increasingly popular owing to algorithmic developments in conjunction with advances in compute capability. Among different approaches for modeling cell-resolved hemodynamics, fluid structure interaction (FSI) algorithms based on the immersed boundary method are frequently employed for coupling separate solvers for the background fluid and the cells within one framework. GPUs can accelerate these simulations; however, both current pre-exascale and future exascale CPU-GPU heterogeneous systems face communication challenges critical to performance and scalability. We describe, to our knowledge, the largest distributed GPU-accelerated FSI simulations of high hematocrit cell-resolved flows with over 17 million red blood cells. We compare scaling on a fat node system with six GPUs per node and on a system with a single GPU per node. Through comparison between the CPU- and GPU-based implementations, we identify the costs of data movement in multiscale multi-grid FSI simulations on heterogeneous systems and show it to be the greatest performance bottleneck on the GPU.

A Combined Deep-Learning and Lattice Boltzmann Model for Segmentation of the Hippocampus in MRI

Segmentation of the hippocampus (HC) in magnetic resonance imaging (MRI) is an essential step for diagnosis and monitoring of several clinical situations such as Alzheimer's disease (AD), schizophrenia and epilepsy. Automatic segmentation of HC structures is challenging due to their small volume, complex shape, low contrast and discontinuous boundaries. The active contour model (ACM) with a statistical shape prior is robust. However, it is difficult to build a shape prior that is general enough to cover all possible shapes of the HC and that suffers the problems of complicated registration of the shape prior and the target object and of low efficiency. In this paper, we propose a semi-automatic model that combines a deep belief network (DBN) and the lattice Boltzmann (LB) method for the segmentation of HC. The training process of DBN consists of unsupervised bottom-up training and supervised training of a top restricted Boltzmann machine (RBM). Given an input image, the trained DBN is utilized to infer the patient-specific shape prior of the HC. The specific shape prior is not only used to determine the initial contour, but is also introduced into the LB model as part of the external force to refine the segmentation. We used a subset of OASIS-1 as the training set and the preliminary release of EADC-ADNI as the testing set. The segmentation results of our method have good correlation and consistency with the manual segmentation results.

Temporal-Spatial Evolution of Kinetic and Thermal Energy Dissipation Rates in a Three-Dimensional Turbulent Rayleigh-Taylor Mixing Zone

In this work, the temporal–spatial evolution of kinetic and thermal energy dissipation rates in three-dimensional (3D) turbulent Rayleigh–Taylor (RT) mixing are investigated numerically by the lattice Boltzmann method. The temperature fields, kinetic and thermal energy dissipation rates with temporal–spatial evolution, the probability density functions, the fractal dimension of mixing interface, spatial scaling law of structure function for the kinetic and the thermal energy dissipation rates in 3D space are analysed in detail to provide an improved physical understanding of the temporal–spatial dissipation-rate characteristic in the 3D turbulent Rayleigh–Taylor mixing zone. Our numerical results indicate that the kinetic and thermal energy dissipation rates are concentrated in areas with large gradients of velocity and temperature with temporal evolution, respectively, which is consistent with the theoretical assumption. However, small scale thermal plumes initially at the section of half vertical height increasingly develop large scale plumes with time evolution. The probability density function tail of thermal energy dissipation gradually rises and approaches the stretched exponent function with temporal evolution. The slope of fractal dimension increases at an early time, however, the fractal dimension for the fluid interfaces is 2.4 at times t/τ ≥ 2, which demonstrates the self-similarity of the turbulent RT mixing zone in 3D space. It is further demonstrated that the second, fourth and sixth-order structure functions for velocity and temperature structure functions have a linear scaling within the inertial range.

Theory, Analysis, and Applications of the Entropic Lattice Boltzmann Model for Compressible Flows

The entropic lattice Boltzmann method for the simulation of compressible flows is studied in detail and new opportunities for extending operating range are explored. We address limitations on the maximum Mach number and temperature range allowed for a given lattice. Solutions to both these problems are presented by modifying the original lattices without increasing the number of discrete velocities and without altering the numerical algorithm. In order to increase the Mach number, we employ shifted lattices while the magnitude of lattice speeds is increased in order to extend the temperature range. Accuracy and efficiency of the shifted lattices are demonstrated with simulations of the supersonic flow field around a diamond-shaped and NACA0012 airfoil, the subsonic, transonic, and supersonic flow field around the Busemann biplane, and the interaction of vortices with a planar shock wave. For the lattices with extended temperature range, the model is validated with the simulation of the Richtmyer-Meshkov instability. We also discuss some key ideas of how to reduce the number of discrete speeds in three-dimensional simulations by pruning of the higher-order lattices, and introduce a new construction of the corresponding guided equilibrium by entropy minimization.

Computed Tomography 3D Super-Resolution with Generative Adversarial Neural Networks: Implications on Unsaturated and Two-Phase Fluid Flow

Fluid flow characteristics are important to assess reservoir performance. Unfortunately, laboratory techniques are inadequate to know these characteristics, which is why numerical methods were developed. Such methods often use computed tomography (CT) scans as input but this technique is plagued by a resolution versus sample size trade-off. Therefore, a super-resolution method using generative adversarial neural networks (GANs) was used to artificially improve the resolution. Firstly, the influence of resolution on pore network properties and single-phase, unsaturated, and two-phase flow was analysed to verify that pores and pore throats become larger on average and surface area decreases with worsening resolution. These observations are reflected in increasingly overestimated single-phase permeability, less moisture uptake at lower capillary pressures, and high residual oil fraction after waterflooding. Therefore, the super-resolution GANs were developed which take low (12 µm) resolution input and increase the resolution to 4 µm, which is compared to the expected high-resolution output. These results better predicted pore network properties and fluid flow properties despite the overestimation of porosity. Relevant small pores and pore surfaces are better resolved thus providing better estimates of unsaturated and two-phase flow which can be heavily influenced by flow along pore boundaries and through smaller pores. This study presents the second case in which GANs were applied to a super-resolution problem on geological materials, but it is the first one to apply it directly on raw CT images and to determine the actual impact of a super-resolution method on fluid predictions.

A voxel image-based pulmonary airflow simulation method with an automatic detection algorithm for airway outlets

Investigations of pulmonary airflows in respiratory systems are important for the diagnostics and treatment of pulmonary diseases. For accurate prediction of the flow field in an airway, a numerical simulation must be conducted using the true geometry from computed tomography (CT) data. Flow simulation is still a difficult task because of the mesh generation process and preprocessing setup procedures. In this study, we developed a voxel image-based simulation method using an automatic detection algorithm for airway outlets to simplify the simulation process and improve its applicability in the medical field. Our approach is based on the lattice Boltzmann method with a topology analysis algorithm, which can preserve all raw information from the original CT images and give an accurate flow field inside the airways. Our method can reproduce the essential flow features inside airways, is highly efficient, and decreases the overall processing time. Thus, it has a great potential for future real-time airflow analyses to provide airflow information to medical experts. HIGHLIGHTS: This paper proposed a voxel image-based simulation method with a novel automatic outlet-selecting algorithm to calculate the velocity and pressure of physiological flows in multi-generation-branched airways. Our approach simplifies the simulation process by automatically applying the boundary conditions to large numbers of outlets and minimizes the time-consuming mesh generation process. Our proposed method has considerable potential for real-time simulations improving the applicability to patient-specific medical diagnostics and treatments.