Pseudoentropic derivation of the regularized lattice Boltzmann method

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.

Asymptotic method for entropic multiple relaxation time model in lattice Boltzmann method

To improve the numerical stability of the lattice Boltzmann method, Karlin et al. [Phys. Rev. E 90, 031302(R) (2014)10.1103/PhysRevE.90.031302] proposed the entropic multiple relaxation time (EMRT) collision model. The idea behind EMRT is to construct an optimal postcollision state by maximizing its local entropy value. The critical step of the EMRT model is to solve the entropy maximization problem under certain constraints, which is often computationally expensive and even not feasible. In this paper, we propose to employ perturbation theory and obtain an asymptotic solution to the maximum entropy state. With mathematical analysis of particular cases under relaxed constraints, we obtain the unperturbed form of the original problem and derive the asymptotic solution. We show that the asymptotic solution well approximates the optimal states; thus, our approach provides an efficient way to solve the constrained maximum entropy problem in the EMRT model. Also, we use the same idea of the EMRT model for the initial condition of the distribution function and propose to leave the entropy function to determine the missing information at the initial nodes. Finally, we numerically verify that the simulation results of the EMRT model obtained via the perturbation theory agree well with the exact solution to the Taylor-Green vortex problem. Furthermore, we also demonstrate that the EMRT model exhibits excellent stability performance for under-resolved simulations in the doubly periodic shear layer flow problem.

Discrete-velocity Boltzmann model: Regularization and linear stability

A discrete-velocity Boltzmann model for a nine-velocity lattice is considered. Compared to the conventional lattice Boltzmann (LB) schemes the collisions for the model are defined explicitly. Space and time discretization of the model is based on the collide and stream method; in addition, the regularization of the collision term is proposed. It is demonstrated that the regularized model can be represented as a two-relaxation-time LB model of a special type. The scheme is compared to the Onsager regularized (a specific filtered Galilean invariant model) and recursively regularized LB equations in terms of stability and dissipation properties, and linear stability analysis is performed. Several numerical experiments are carried out: double shear layer, lid-driven cavity flow, and propagation of acoustic and shear waves are considered for different grid resolutions, Mach and Reynolds numbers. It is shown that free parameters in the model corresponding to collision cross sections can be adjusted in such a way that the dissipation and stability properties can be controlled.

Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence

Multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) based on orthogonal moments exhibit lattice Mach number dependent instabilities in diffusive scaling. The present work renders an explicit formulation of stability sets for orthogonal moment MRT LBM. The stability sets are defined via the spectral radius of linearized amplification matrices of the MRT collision operator with variable relaxation frequencies. Numerical investigations are carried out for the three-dimensional Taylor-Green vortex benchmark at Reynolds number 1600. Extensive brute force computations of specific relaxation frequency ranges for the full test case are opposed to the von Neumann stability set prediction. Based on that, we prove numerically that a scan over the full wave space, including scaled mean flow variations, is required to draw conclusions on the overall stability of LBM in turbulent flow simulations. Furthermore, the von Neumann results show that a grid dependence is hardly possible to include in the notion of linear stability for LBM. Lastly, via brute force stability investigations based on empirical data from a total number of 22 696 simulations, the existence of a deterministic influence of the grid resolution is deduced. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Enhanced multi-relaxation-time lattice Boltzmann model by entropic stabilizers

The difficulty of choice of relaxation rates in multi-relaxation-time lattice Boltzmann model (MRT-LBM) is surmounted by solution of least-square problem of entropic stabilizer equations. Relaxation rates in the enhanced MRT-LBM are evolving with time rather than remain constants. To derive entropic stabilizer equations, nonequilibrium population is split into different modes in terms of column vectors in the inverse transform matrix. The entropic stabilizer equations are achieved by minimization of H-function. Different moment representations in MRT-LBM, such as Gram-Schmidt orthogonal moment, natural moment, and central moment, are tested for double periodic shear flow, shock tube problem, and lid-driven cavity flow, which demonstrates the potential of enhanced MRT-LBM.

Grid refinement in the three-dimensional hybrid recursive regularized lattice Boltzmann method for compressible aerodynamics

Grid refinement techniques are of paramount importance for computational fluid dynamics approaches relying on the use of Cartesian grids. This is especially true of solvers dedicated to aerodynamics, in which the capture of thin shear layers require the use of small cells. In this paper, a three-dimensional grid refinement technique is developed within the framework of hybrid recursive regularized lattice Boltzmann method (HRR-LBM) for compressible high-speed flows, which is an efficient collide-stream-type method on a compact D3Q19 stencil. The proposed method is successfully assessed considering several test cases, namely, an isentropic vortex propagating through transition interface, shock-vortex interaction with intersection between grid refinement interface and shock corrugation, and transonic flows over three-dimensional DLR-M6 wing with seven levels of grid refinement.