Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics

Preface to the Special Issue on “Control, Optimization, and Mathematical Modeling of Complex Systems”

Complex systems have long been an integral part of modern life and can be encountered everywhere [...]

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.

Cross-Platform GPU-Based Implementation of Lattice Boltzmann Method Solver Using ArrayFire Library

This paper deals with the design and implementation of cross-platform, D2Q9-BGK and D3Q27-MRT, lattice Boltzmann method solver for 2D and 3D flows developed with ArrayFire library for high-performance computing. The solver leverages ArrayFire’s just-in-time compilation engine for compiling high-level code into optimized kernels for both CUDA and OpenCL GPU backends. We also provide C++ and Rust implementations and show that it is possible to produce fast cross-platform lattice Boltzmann method simulations with minimal code, effectively less than 90 lines of code. An illustrative benchmarks (lid-driven cavity and Kármán vortex street) for single and double precision floating-point simulations on 4 different GPUs are provided.