1
|
Petkantchin R, Rousseau A, Eker O, Zouaoui Boudjeltia K, Raynaud F, Chopard B. A simplified mesoscale 3D model for characterizing fibrinolysis under flow conditions. Sci Rep 2023; 13:13681. [PMID: 37608073 PMCID: PMC10444897 DOI: 10.1038/s41598-023-40973-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Accepted: 08/19/2023] [Indexed: 08/24/2023] Open
Abstract
One of the routine clinical treatments to eliminate ischemic stroke thrombi is injecting a biochemical product into the patient's bloodstream, which breaks down the thrombi's fibrin fibers: intravenous or intravascular thrombolysis. However, this procedure is not without risk for the patient; the worst circumstances can cause a brain hemorrhage or embolism that can be fatal. Improvement in patient management drastically reduced these risks, and patients who benefited from thrombolysis soon after the onset of the stroke have a significantly better 3-month prognosis, but treatment success is highly variable. The causes of this variability remain unclear, and it is likely that some fundamental aspects still require thorough investigations. For that reason, we conducted in vitro flow-driven fibrinolysis experiments to study pure fibrin thrombi breakdown in controlled conditions and observed that the lysis front evolved non-linearly in time. To understand these results, we developed an analytical 1D lysis model in which the thrombus is considered a porous medium. The lytic cascade is reduced to a second-order reaction involving fibrin and a surrogate pro-fibrinolytic agent. The model was able to reproduce the observed lysis evolution under the assumptions of constant fluid velocity and lysis occurring only at the front. For adding complexity, such as clot heterogeneity or complex flow conditions, we propose a 3-dimensional mesoscopic numerical model of blood flow and fibrinolysis, which validates the analytical model's results. Such a numerical model could help us better understand the spatial evolution of the thrombi breakdown, extract the most relevant physiological parameters to lysis efficiency, and possibly explain the failure of the clinical treatment. These findings suggest that even though real-world fibrinolysis is a complex biological process, a simplified model can recover the main features of lysis evolution.
Collapse
Affiliation(s)
- Remy Petkantchin
- Scientific and Parallel Computing Group, Computer Science Department, University of Geneva, Geneva, Switzerland.
- Complex System Modeling Group, Computer Science Department, University of Geneva, Geneva, Switzerland.
| | - Alexandre Rousseau
- Laboratory of Experimental Medicine (ULB222), Faculty of Medicine, Université libre de Bruxelles, CHU de Charleroi, Charleroi, Belgium
| | - Omer Eker
- Department of Neuroradiology, Hôpital Pierre Wertheimer, Hospices Civils de Lyon, Lyon, France
- CREATIS Laboratory, UMR 5220, U1206, Université Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, Lyon, France
| | - Karim Zouaoui Boudjeltia
- Laboratory of Experimental Medicine (ULB222), Faculty of Medicine, Université libre de Bruxelles, CHU de Charleroi, Charleroi, Belgium
| | - Franck Raynaud
- Scientific and Parallel Computing Group, Computer Science Department, University of Geneva, Geneva, Switzerland
- Complex System Modeling Group, Computer Science Department, University of Geneva, Geneva, Switzerland
| | - Bastien Chopard
- Scientific and Parallel Computing Group, Computer Science Department, University of Geneva, Geneva, Switzerland
- Complex System Modeling Group, Computer Science Department, University of Geneva, Geneva, Switzerland
| |
Collapse
|
2
|
Gu J, Ren Q, Tao M, Han Y, Zhang L. Permeability Coefficient of Concrete under Complex Stress States. MATERIALS (BASEL, SWITZERLAND) 2023; 16:4368. [PMID: 37374552 DOI: 10.3390/ma16124368] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Revised: 05/26/2023] [Accepted: 06/12/2023] [Indexed: 06/29/2023]
Abstract
Hydraulic structures are typically subjected to long-term hydraulic loading, and concrete-the main material of structures-may suffer from cracking damage and seepage failure, which can threaten the safety of hydraulic structures. In order to assess the safety of hydraulic concrete structures and realize the accurate analysis of the whole failure process of hydraulic concrete structures under the coupling effect of seepage and stress, it is vital to comprehend the variation law of concrete permeability coefficients under complex stress states. In this paper, several concrete samples were prepared, designed for loading conditions of confining pressures and seepage pressures in the first stage, and axial pressures in the later stage, to carry out the permeability experiment of concrete materials under multi-axial loading, followed by the relationships between the permeability coefficients and axial strain, and the confining and seepage pressures were revealed accordingly. In addition, during the application of axial pressure, the whole process of seepage-stress coupling was divided into four stages, describing the permeability variation law of each stage and analyzing the causes of its formation. The exponential relationship between the permeability coefficient and volume strain was established, which can serve as a scientific basis for the determination of permeability coefficients in the analysis of the whole failure process of concrete seepage-stress coupling. Finally, this relationship formula was applied to numerical simulation to verify the applicability of the above experimental results in the numerical simulation analysis of concrete seepage-stress coupling.
Collapse
Affiliation(s)
- Jiafeng Gu
- College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China
| | - Qingwen Ren
- Department of Engineering Mechanics, Hohai University, Nanjing 211100, China
| | - Mei Tao
- College of Civil and Architecture Engineering, Chuzhou University, Chuzhou 239000, China
| | - Yan Han
- Department of Engineering Mechanics, Hohai University, Nanjing 211100, China
| | - Linfei Zhang
- College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China
| |
Collapse
|
3
|
Gao Y, Zhou W, Wen Z, Dou R, Liu X. Meso-scale Simulation of Li–O2 Battery Discharge Process by an Improved Lattice Boltzmann Method. Electrochim Acta 2023. [DOI: 10.1016/j.electacta.2023.141880] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
|
4
|
Numerical Modelling of Reactive Flows through Porous Media. GEOSCIENCES 2022. [DOI: 10.3390/geosciences12040153] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We consider a lattice Boltzmann (LB) model to solve the coupled Navier–Stokes and advection–diffusion equation with reactive boundary conditions at the interface between fluid and solid domains. The reactive boundary condition results in the position of the boundary changing continuously, and so boundary nodes may be partially filled with fluid at any instant. We develop the LB boundary conditions for both the velocity and concentration fields in the presence of partially filled boundary nodes and then validate this algorithm on some test cases—the Stefan problem for diffusion-dominated dissolution and kinetic-dominated dissolution. It is shown that the developed model agrees well with analytic results, so that they can be used for more general boundaries of arbitrary shape. Numerical simulations in three dimensions are then carried out on demonstration problems at various Peclet numbers to elucidate the transport mechanisms and their influence on solid grain dissolution.
Collapse
|
5
|
Ibrahim E, Jouini MS, Bouchaala F, Gomes J. Simulation and Validation of Porosity and Permeability of Synthetic and Real Rock Models Using Three-Dimensional Printing and Digital Rock Physics. ACS OMEGA 2021; 6:31775-31781. [PMID: 34870000 PMCID: PMC8638297 DOI: 10.1021/acsomega.1c04429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Accepted: 11/03/2021] [Indexed: 05/13/2023]
Abstract
A standard digital rock physics workflow aims to simulate petrophysical properties of rock samples using few millimeter size subsets scanned with X-ray microtomography at a high resolution of around 1 μm. The workflow is mainly based on image analysis and simulation procedures at a subset scale leading to potential uncertainties and errors that cannot be quantified experimentally. To overcome the gap between scales, we propose to integrate three-dimensional (3D) printing technology to generate enlarged subsets at a scale where experimental measurements are feasible to validate simulated results. In this study, we 3D printed synthetic and real samples and compared digital and experimental rock properties. The most challenging phase in the workflow consists of the difficulties encountered while cleaning the 3D printed samples to remove the support material. Results for subsets extracted from synthetic, sandstone, and carbonate samples showed good agreement between digital and experimental measurements for porosity values less than 12% and a range of permeability values between 100 and 2000 mD.
Collapse
Affiliation(s)
- Ezdeen
R. Ibrahim
- Department
of Geosciences, Khalifa University, Abu Dhabi 127788, United Arab Emirates
| | - Mohamed Soufiane Jouini
- Department
of Mathematics, Khalifa University, Abu Dhabi 127788, United Arab Emirates
- . Tel.: +971 2 312 3306; +971503170946
| | - Fateh Bouchaala
- Department
of Geosciences, Khalifa University, Abu Dhabi 127788, United Arab Emirates
| | - Jorge Gomes
- Abu
Dhabi National Oil Company, Abu Dhabi 898, United Arab Emirates
| |
Collapse
|
6
|
González-Flores MI, Torres AA, Lebrecht W, Ramirez-Pastor AJ. Site-bond percolation in two-dimensional kagome lattices: Analytical approach and numerical simulations. Phys Rev E 2021; 104:014130. [PMID: 34412224 DOI: 10.1103/physreve.104.014130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2021] [Accepted: 06/21/2021] [Indexed: 06/13/2023]
Abstract
The site-bond percolation problem in two-dimensional kagome lattices has been studied by means of theoretical modeling and numerical simulations. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as S∩B and S∪B) have been considered. In S∩B (S∪B), two points are connected if a sequence of occupied sites and (or) bonds joins them. Analytical and simulation approaches, supplemented by analysis using finite-size scaling theory, were used to calculate the phase boundaries between the percolating and nonpercolating regions, thus determining the complete phase diagram of the system in the (p_{s},p_{b}) space. In the case of the S∩B model, the obtained results are in excellent agreement with previous theoretical and numerical predictions. In the case of the S∪B model, the limiting curve separating percolating and nonpercolating regions is reported here.
Collapse
Affiliation(s)
- M I González-Flores
- Departamento de Física, Universidad de La Frontera, Casilla 54-D, Temuco, Chile
| | - A A Torres
- Departamento de Física, Instituto de Física Aplicada (INFAP), Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW San Luis, Argentina
| | - W Lebrecht
- Departamento de Física, Universidad de La Frontera, Casilla 54-D, Temuco, Chile
| | - A J Ramirez-Pastor
- Departamento de Física, Instituto de Física Aplicada (INFAP), Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW San Luis, Argentina
| |
Collapse
|
7
|
Phase-Field Simulation of Imbibition for the Matrix-Fracture of Tight Oil Reservoirs Considering Temperature Change. WATER 2021. [DOI: 10.3390/w13071004] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Injection water temperature is often different from that of the reservoir during water injection development in the tight reservoir. Temperature change causes different fluid properties and oil-water interface properties, which further affects the imbibition process. In this paper, a matrix-fracture non-isothermal oil-water imbibition flow model in tight reservoirs is established and solved by the finite element method based on the phase-field method. The ideal inhomogeneous rock structure model was used to study the influence of a single factor on the imbibition. The actual rock structure model was used to study the influence of temperature. The mechanism of temperature influence in the process of imbibition is studied from the micro-level. It is found that the imbibition of matrix-fracture is a process in which the water enters the matrix along with the small pores, and the oil is driven into the macropores and then into the fractures. Temperature affects the imbibition process by changing the oil-water contact angle, oil-water interfacial tension, and oil-water viscosity ratio. Reducing oil-water contact angle and oil-water viscosity ratio and increasing oil-water interfacial tension are conducive to the imbibition process. The increase in injection water temperature is usually beneficial to the occurrence of the imbibition. Moreover, the actual core structure imbibition degree is often lower than that of the ideal core structure. The inhomogeneous distribution of rock particles has a significant influence on imbibition. This study provides microscale theoretical support for seeking reasonable injection velocity, pressure gradient, injection temperature, and well-shutting time in the field process. It provides a reference for the formulation of field process parameters.
Collapse
|
8
|
Ramirez LS, Centres PM, Ramirez-Pastor AJ. Percolation phase transition by removal of k^{2}-mers from fully occupied lattices. Phys Rev E 2019; 100:032105. [PMID: 31640014 DOI: 10.1103/physreve.100.032105] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2019] [Indexed: 11/07/2022]
Abstract
Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse site percolation by the removal of k×k square tiles (k^{2}-mers) from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by occupied sites. Then the system is diluted by removing k^{2}-mers of occupied sites from the lattice following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be removed due to the absence of occupied sites clusters of appropriate size and shape. The central idea of this paper is based on finding the maximum concentration of occupied sites, p_{c,k}, for which the connectivity disappears. This particular value of the concentration is called the inverse percolation threshold and determines a well-defined geometrical phase transition in the system. The results obtained for p_{c,k} show that the inverse percolation threshold is a decreasing function of k in the range 1≤k≤4. For k≥5, all jammed configurations are percolating states, and consequently, there is no nonpercolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed sites is reached. The jamming exponent ν_{j} was measured, being ν_{j}=1 regardless of the size k considered. In addition, the accurate determination of the critical exponents ν, β, and γ reveals that the percolation phase transition involved in the system, which occurs for k varying between one and four, has the same universality class as the standard percolation problem.
Collapse
Affiliation(s)
- L S Ramirez
- Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW, San Luis, Argentina
| | - P M Centres
- Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW, San Luis, Argentina
| | - A J Ramirez-Pastor
- Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW, San Luis, Argentina
| |
Collapse
|
9
|
Baveye PC, Otten W, Kravchenko A, Balseiro-Romero M, Beckers É, Chalhoub M, Darnault C, Eickhorst T, Garnier P, Hapca S, Kiranyaz S, Monga O, Mueller CW, Nunan N, Pot V, Schlüter S, Schmidt H, Vogel HJ. Emergent Properties of Microbial Activity in Heterogeneous Soil Microenvironments: Different Research Approaches Are Slowly Converging, Yet Major Challenges Remain. Front Microbiol 2018; 9:1929. [PMID: 30210462 PMCID: PMC6119716 DOI: 10.3389/fmicb.2018.01929] [Citation(s) in RCA: 125] [Impact Index Per Article: 20.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2018] [Accepted: 07/30/2018] [Indexed: 01/17/2023] Open
Abstract
Over the last 60 years, soil microbiologists have accumulated a wealth of experimental data showing that the bulk, macroscopic parameters (e.g., granulometry, pH, soil organic matter, and biomass contents) commonly used to characterize soils provide insufficient information to describe quantitatively the activity of soil microorganisms and some of its outcomes, like the emission of greenhouse gasses. Clearly, new, more appropriate macroscopic parameters are needed, which reflect better the spatial heterogeneity of soils at the microscale (i.e., the pore scale) that is commensurate with the habitat of many microorganisms. For a long time, spectroscopic and microscopic tools were lacking to quantify processes at that scale, but major technological advances over the last 15 years have made suitable equipment available to researchers. In this context, the objective of the present article is to review progress achieved to date in the significant research program that has ensued. This program can be rationalized as a sequence of steps, namely the quantification and modeling of the physical-, (bio)chemical-, and microbiological properties of soils, the integration of these different perspectives into a unified theory, its upscaling to the macroscopic scale, and, eventually, the development of new approaches to measure macroscopic soil characteristics. At this stage, significant progress has been achieved on the physical front, and to a lesser extent on the (bio)chemical one as well, both in terms of experiments and modeling. With regard to the microbial aspects, although a lot of work has been devoted to the modeling of bacterial and fungal activity in soils at the pore scale, the appropriateness of model assumptions cannot be readily assessed because of the scarcity of relevant experimental data. For significant progress to be made, it is crucial to make sure that research on the microbial components of soil systems does not keep lagging behind the work on the physical and (bio)chemical characteristics. Concerning the subsequent steps in the program, very little integration of the various disciplinary perspectives has occurred so far, and, as a result, researchers have not yet been able to tackle the scaling up to the macroscopic level. Many challenges, some of them daunting, remain on the path ahead. Fortunately, a number of these challenges may be resolved by brand new measuring equipment that will become commercially available in the very near future.
Collapse
Affiliation(s)
- Philippe C. Baveye
- UMR ECOSYS, AgroParisTech, Université Paris-Saclay, Thiverval-Grignon, rance
| | - Wilfred Otten
- School of Water, Energy and Environment, Cranfield University, Cranfield, United Kingdom
| | - Alexandra Kravchenko
- Department of Plant, Soil and Microbial Sciences, Michigan State University, East Lansing, MI, United States
| | - María Balseiro-Romero
- UMR ECOSYS, AgroParisTech, Université Paris-Saclay, Thiverval-Grignon, rance
- Department of Soil Science and Agricultural Chemistry, Centre for Research in Environmental Technologies, Universidade de Santiago de Compostela, Santiago de Compostela, Spain
| | - Éléonore Beckers
- Soil–Water–Plant Exchanges, Terra Research Centre, BIOSE, Gembloux Agro-Bio Tech, University of Liège, Gembloux, Belgium
| | - Maha Chalhoub
- UMR ECOSYS, INRA, Université Paris-Saclay, Thiverval-Grignon, France
| | - Christophe Darnault
- Laboratory of Hydrogeoscience and Biological Engineering, L.G. Rich Environmental Laboratory, Department of Environmental Engineering and Earth Sciences, Clemson University, Clemson, SC, United States
| | - Thilo Eickhorst
- Faculty 2 Biology/Chemistry, University of Bremen, Bremen, Germany
| | - Patricia Garnier
- UMR ECOSYS, INRA, Université Paris-Saclay, Thiverval-Grignon, France
| | - Simona Hapca
- Dundee Epidemiology and Biostatistics Unit, School of Medicine, University of Dundee, Dundee, United Kingdom
| | - Serkan Kiranyaz
- Department of Electrical Engineering, Qatar University, Doha, Qatar
| | - Olivier Monga
- Institut de Recherche pour le Développement, Bondy, France
| | - Carsten W. Mueller
- Lehrstuhl für Bodenkunde, Technical University of Munich, Freising, Germany
| | - Naoise Nunan
- Institute of Ecology and Environmental Sciences – Paris, Sorbonne Universités, CNRS, IRD, INRA, P7, UPEC, Paris, France
| | - Valérie Pot
- UMR ECOSYS, INRA, Université Paris-Saclay, Thiverval-Grignon, France
| | - Steffen Schlüter
- Soil System Science, Helmholtz-Zentrum für Umweltforschung GmbH – UFZ, Leipzig, Germany
| | - Hannes Schmidt
- Terrestrial Ecosystem Research, Department of Microbiology and Ecosystem Science, Research Network ‘Chemistry meets Microbiology’, University of Vienna, Vienna, Austria
| | - Hans-Jörg Vogel
- Soil System Science, Helmholtz-Zentrum für Umweltforschung GmbH – UFZ, Leipzig, Germany
- Institute of Soil Science and Plant Nutrition, Martin Luther University of Halle-Wittenberg, Halle, Germany
| |
Collapse
|
10
|
|
11
|
Pereira GG, Wu B, Ahmed S. Lattice Boltzmann heat transfer model for permeable voxels. Phys Rev E 2017; 96:063108. [PMID: 29347372 DOI: 10.1103/physreve.96.063108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2017] [Indexed: 06/07/2023]
Abstract
We develop a gray-scale lattice Boltzmann (LB) model to study fluid flow combined with heat transfer for flow through porous media where voxels may be partially solid (or void). Heat transfer in rocks may lead to deformation, which in turn can modulate the fluid flow and so has significant contribution to rock permeability. The LB temperature field is compared to a finite difference solution of the continuum partial differential equations for fluid flow in a channel. Excellent quantitative agreement is found for both Poiseuille channel flow and Brinkman flow. The LB model is then applied to sample porous media such as packed beds and also more realistic sandstone rock sample, and both the convective and diffusive regimes are recovered when varying the thermal diffusivity. It is found that while the rock permeability can be comparatively small (order milli-Darcy), the temperature field can show significant variation depending on the thermal convection of the fluid. This LB method has significant advantages over other numerical methods such as finite and boundary element methods in dealing with coupled fluid flow and heat transfer in rocks which have irregular and nonsmooth pore spaces.
Collapse
Affiliation(s)
- Gerald G Pereira
- CSIRO Computational Modelling, Private Bag 10, Clayton South, 3169, Australia
| | - Bisheng Wu
- CSIRO Energy, Private Bag 10, Clayton South, 3169, Australia
| | - Shakil Ahmed
- CSIRO Energy, 26 Dick Perry Avenue, Kensington, WA6151, Australia
| |
Collapse
|
12
|
Pereira GG. Grayscale lattice Boltzmann model for multiphase heterogeneous flow through porous media. Phys Rev E 2016; 93:063301. [PMID: 27415381 DOI: 10.1103/physreve.93.063301] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2015] [Indexed: 11/07/2022]
Abstract
The grayscale lattice Boltzmann (LB) model has been recently developed to model single-phase fluid flow through heterogeneous porous media. Flow is allowed in each voxel but the degree of flow depends on that voxel's resistivity to fluid motion. Here we extend the grayscale LB model to multiphase, immiscible flow. The new model is outlined and then applied to a number of test cases, which show good agreement with theory. This method is subsequently used to model the important case where each voxel may have a different resistance to each particular fluid that is passing through it. Finally, the method is applied to model fluid flow through real porous media to demonstrate its capability. Both the capillary and viscous flow regimes are recovered in these simulations.
Collapse
Affiliation(s)
- Gerald G Pereira
- CSIRO Computational Modelling, Private Bag 10, Clayton South, 3169, Australia
| |
Collapse
|
13
|
Stokes–Brinkman–Darcy Solutions of Bimodal Porous Flow Across Periodic Array of Permeable Cylindrical Inclusions: Cell Model, Lubrication Theory and LBM/FEM Numerical Simulations. Transp Porous Media 2016. [DOI: 10.1007/s11242-016-0628-8] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
14
|
Ginzburg I, Silva G, Talon L. Analysis and improvement of Brinkman lattice Boltzmann schemes: bulk, boundary, interface. Similarity and distinctness with finite elements in heterogeneous porous media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:023307. [PMID: 25768636 DOI: 10.1103/physreve.91.023307] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2014] [Indexed: 06/04/2023]
Abstract
This work focuses on the numerical solution of the Stokes-Brinkman equation for a voxel-type porous-media grid, resolved by one to eight spacings per permeability contrast of 1 to 10 orders in magnitude. It is first analytically demonstrated that the lattice Boltzmann method (LBM) and the linear-finite-element method (FEM) both suffer from the viscosity correction induced by the linear variation of the resistance with the velocity. This numerical artefact may lead to an apparent negative viscosity in low-permeable blocks, inducing spurious velocity oscillations. The two-relaxation-times (TRT) LBM may control this effect thanks to free-tunable two-rates combination Λ. Moreover, the Brinkman-force-based BF-TRT schemes may maintain the nondimensional Darcy group and produce viscosity-independent permeability provided that the spatial distribution of Λ is fixed independently of the kinematic viscosity. Such a property is lost not only in the BF-BGK scheme but also by "partial bounce-back" TRT gray models, as shown in this work. Further, we propose a consistent and improved IBF-TRT model which vanishes viscosity correction via simple specific adjusting of the viscous-mode relaxation rate to local permeability value. This prevents the model from velocity fluctuations and, in parallel, improves for effective permeability measurements, from porous channel to multidimensions. The framework of our exact analysis employs a symbolic approach developed for both LBM and FEM in single and stratified, unconfined, and bounded channels. It shows that even with similar bulk discretization, BF, IBF, and FEM may manifest quite different velocity profiles on the coarse grids due to their intrinsic contrasts in the setting of interface continuity and no-slip conditions. While FEM enforces them on the grid vertexes, the LBM prescribes them implicitly. We derive effective LBM continuity conditions and show that the heterogeneous viscosity correction impacts them, a property also shared by FEM for shear stress. But, in contrast with FEM, effective velocity conditions in LBM give rise to slip velocity jumps which depend on (i) neighbor permeability values, (ii) resolution, and (iii) control parameter Λ, ranging its reliable values from Poiseuille bounce-back solution in open flow to zero in Darcy's limit. We suggest an "upscaling" algorithm for Λ, from multilayers to multidimensions in random extremely dispersive samples. Finally, on the positive side for LBM besides its overall versatility, the implicit boundary layers allow for smooth accommodation of the flat discontinuous Darcy profiles, quite deficient in FEM.
Collapse
Affiliation(s)
- Irina Ginzburg
- Irstea, Antony Regional Centre, HBAN, 1 rue Pierre-Gilles de Gennes CS 10030, 92761 Antony cedex, France
| | - Goncalo Silva
- Irstea/Cemagref, Antony Regional Centre, HBAN, 1 rue Pierre-Gilles de Gennes CS 10030, 92761 Antony cedex, France
| | - Laurent Talon
- CNRS (UMR 7608), Laboratoire FAST, Batiment 502, Campus Universitaire, 91405 Orsay, France
| |
Collapse
|