Entropic Lattice Boltzmann Method based high Reynolds number flow simulation using CUDA on GPU

Abstract

Entropic Lattice Boltzmann Method (ELBM) is used for the stable computational simulation of high Reynolds number fluid flows, due to it alleviates the obstacle of numerical instabilities by restoring the second law of thermodynamics (Boltzmann’s H-theorem). In general, this stability is gained at the price of some computational overhead, associated with the requirement of adjusting the local relaxation parameter of the standard Lattice Boltzmann Method (LBM) in such a way as to guarantee compliance with H-theorem. In this paper, we present a very efficient implementation strategy for ELBM based high Reynolds number flow simulation on nVIDIA graphics processing unit (GPU) with optimization approaches. Some algorithms for H-α solver on GPU which solve the relaxation adjusting parameter are also proposed in our study. We demonstrate the ELBM-GPU parallel approach for fluid flows simulation which can reduce the computational cost of ELBM implementation and obtain an excellent performance. Meanwhile, we find that the direct approximate method of parameter solution is more efficient than other methods on the whole. The results show that: (1) the whole ELBM-GPU implementation results in average speedups of 3.14 over the single-core ELBM-CPU result; (2) comparison of two types of methods for H-α solver, the direct approximate method can save an average 31.7% of computation time than the iteration method; and (3) the implementation of ELBM on GPU allows us to achieve up to 50% global memory bandwidth utilization ratio.