An Efficient GPU Algorithm for Lattice Boltzmann Method on Sparse Complex Geometries

Many fluid flow problems, such as the porous media, arterial blood flow and tissue fluid, contain sparse complex geometries. Although the lattice Boltzmann method is good at dealing with the complex boundaries, these sparse complex geometries cause the low computational performance and high memory consumption when the graphics processing unit (GPU) is used to accelerate the numerical computation. These problems would be addressed by compact memory layout, sophisticated memory access and enhanced thread utilization. This paper proposes a GPU-based algorithm to improve the lattice Boltzmann simulations with sparse complex geometries. An access pattern for a single set of distribution functions together with a semi-direct addressing is adopted to reduce memory consumption, while a collected structure of arrays is employed to enhance memory access efficiency. Furthermore, an address index array and a node classification coding scheme are employed to improve the GPU thread utilization ratio and reduce the GPU global memory access, respectively. The accuracy and mesh-independence has been verified by the numerical simulations of Poiseuille flow and porous media flow with face-centered filled spheres. The present algorithm has a significantly lower memory consumption than those based on direct or indirect addressing schemes. It improves the computational performance by several times compared to the other algorithms on the common GPU hardware.