Compressible lattice Boltzmann simulations on high‐performance and low‐cost GeForce GPU

Abstract

The feasibility of compressible lattice Boltzmann simulations on high-performance and low-cost NVIDIA GeForce GPU is studied to enhance computational efficiency of compressible lattice Boltzmann by using much cheaper computing hardware. The NVIDIA GeForce GTX 1080 GPU, which has similar single precision operation computing performance with NVIDIA scientific computational Tesla K80 GPU and much lower price (seven to ten times) than the latter, is used in this work. The problem of GeForce GPUs is with low double precision operation performance and lack of error-correcting code memory, which will influence the accuracy of compressible lattice Boltzmann simulations. To evaluate its feasibility, the double-distribution-function lattice Boltzmann method is adopted for compressible fluid flows. Three typical compressible problems are tested, ie, the Riemann problem, the regular shock reflection problem, and the supersonic boundary layer problem. The results by GeForce GPU with single precision operation have numerical fluctuations in the simulations with shock waves. Moreover, GeForce GPUs have similar numerical accuracy with CPUs in the regular shock reflection problem and supersonic boundary layer problem. KEYWORDS compressible flows, GPU, lattice Boltzmann method, parallel computing, shock waves INTRODUCTIONThe lattice Boltzmann method (LBM) 1,2 is a promising mesoscopic computational fluid dynamic method. It has been widely applied to various incompressible fluid flow problems, 3-7 and shows great potential for complex phenomena due to its mesoscopic features and highly efficient parallel computing. 8,9 The special streaming-collision scheme and the equilibrium distribution function of the standard LBM make it difficult to describe compressible fluid flows, which are ubiquitous in explosion physics, aerophysics, astrophysics, etc. The solving scheme and the equilibrium distribution function need to be developed for a compressible LBM. The finite-difference scheme, which can solve the problem of the streaming-collision scheme, is popular in the compressible LBM. Kataoka and Tsutahara 10 proposed a compressible model for Navier-Stokes equations, which has an adjustable specific heat ratio. Watari 11 also proposed a model for Navier-Stokes with a flexible specific heat ratio. They are within the low Mach number limit. Qu et al 12 established a lattice Boltzmann (LB) model for inviscid compressible flows, in which a circular function is applied instead of the conventional Maxwellian distribution function. This model has ability for simulation of compressible flows at a high Mach number. Li et al 13,14 introduced Qu et al's model into a coupled double-distribution-function (DDF) LB scheme for compressible flows with adjustable specific heat ratio and Prandtl number. Wang et al 15 presented another DDF LB model for compressible flows with a different total energy distribution function. Chen et al 16,17 proposed a multiple-relaxation-time (MRT) LB model for compressible flows. Gan et al 18 presented a simple and general ap...