Simulation And GPU Parallel Of 3D Groundwater Flow Based On Lattice Boltzmann Method

Lattice Boltzmann Method(LBM)is a mesoscopic method between the traditional macroscopic methods and the traditional microscopic methods to solve the partial differential equations(PDE).The traditional macroscopic methods need to construct a massive system of linear equations,which is hard to solve and the traditional microscopic methods can not show the flow details.For the traditional microscopic methods,they are not feasible to use on the current computers,even the super computers,because they work in such a small scale.Lattice Boltzmann Methods make up the disadvantages of the traditional macroscopic methods and the traditional microscopic methods,and own the advantage of convenient boundary conditions treatments and can be parallelized.There are two models based on Lattice Boltzmann Method,the Lattice BGK(LBGK)or Single-Relaxation-Time(SRT)model and the Multi-Relaxation-Time(MRT)model.LBGK-LBM model has simulated on single relaxation time while MRT-LBM model simulates in different directions.The MRT has a more rapid convergence speed than the LBGK-LBM,although the MRT-LBM has more calculations than the LBGK-LBM in one iteration because of the operations about the matrices and the vectors.Many PDE can be solved by using the LBGK model and the MRT model.This paper simulated three-dimensional(3D)groundwater flow in porous media based on Lattice Boltzmann Methods.The results of the experiments showed the feasibility and the accuracy,the errors between the experimental results and the theoretical values were quite small.MRT-LBM model had more rapid convergence,and less computing time than the LBGK-LBM model.The MRT-LBM model for solving 3D groundwater flow was parallelized on GPUs,and CUDA was used.Each thread operated each lattice in the paper and the experimental results showed the great speedup.As the lattices scales got bigger and bigger,the speedups between GPU and CPU became larger and larger.To get more speedups and satisfy the increase number of lattices,we used OpenMP architecture to calculate MRT-LBM on multi-GPUs.OpenMP firstly made the CPU cores work in parallel and then each CPU core controlled each GPU.So the 3D groundwater flow based on MRT-LBM was implementaed on multi-GPUs by combining the two parallel architectures,CUDA and OpenMP.The number of threads used in parallel increased with the increase of the number of GPUs.The experimental results showed that the more the number of GPUs were used,the larger the speedups could be got.