GPU-Accelerated High-Order Regularized Lattice Boltzmann Simulations of Lid-Driven Cavity Flows

Resumo

We use high-order moment approximations within the Moment Representation lattice Boltzmann Method (MR-LBM) to simulate lid-driven cavity (LDC) flows, assessing the performance of D3Q19 and D3Q27 velocity stencils. Numerical experiments were conducted for Reynolds numbers ranging from 3,200 to 10,000 as part of the validation process. The MR-LBM implementation utilizes a regularized formulation of the lattice Boltzmann equation combined with the Bhatnagar-Gross-Krook (BGK) collision operator. Particle populations are reconstructed based on moments of the distribution function, with third and fourth-order moments approximated through lower-order moment relationships. This approach enables extended regularization up to fourth-order terms, significantly enhancing numerical stability and accuracy without compromising computational efficiency. Additionally, the incompressible regularized boundary condition (IRBC) was adopted. The systematic expansion of the distribution function to arbitrary orders was facilitated by Hermite polynomials, which provided a recursive framework for computing high-order terms. Consequently, the developed LBM framework accurately captured flow features at high Reynolds numbers. Leveraging the explicit nature of LBM equations allowed straightforward and efficient implementation on graphics processing units (GPUs), enabling highly accurate large-scale simulations with fine grid resolutions. Mean and root mean square (RMS) velocity profiles from the simulations demonstrated good agreement with experimental data from the literature. Building upon this validation, the methodology was extended to higher Reynolds numbers—specifically 10,000, 15,000, and 50,000—highlighting the robustness and versatility of the proposed MR-LBM approach across a wide range of complex flow conditions.