GPU-accelerated volumetric lattice Boltzmann method for porous media flow

The volumetric lattice Boltzmann method (VLBM) has been recently developed and validated for dealing with flows in complex geometries. To reveal the intricate and arbitrary porous media skeleton, VLBM categorizes the computational domain into fluid, solid, and boundary cells by introducing a volumetric parameter P((x) over right arrow), through which the lattice Boltzmann equations are self-regularized. As a result, the no-slip bounce-back boundary condition at the inter walls is integrated in the streaming term. Since its data structure is aligned and kernel pattern is clear, VLBM is ideally suited for GPU parallelization. Using the P((x) over right arrow) in the streaming operation, branch diverse can be effectively decreased. In this paper, we use several optimization methods, such as memory arrangement and kernel design, to maximize the performance of parallelization for VLBM. As an application, we simulated petroleum flow in a digital sandstone with two resolutions, 256(3) and 256(2) x 512, and evaluated its permeability. The best parallel performance reaches 808.7 MLUPS (Million Lattice Updates Per Second), which is 1421.3-times speedup compared with the serial computation with allocated memory.