Comparison of Lattice-Boltzmann and finite difference solvers

Lattice-Boltzmann methods (LBMs) have improved considerably over the last three decades and are used for many low Mach-number applications. The aim of the present effort is to understand and compare LBMs with FDMs. In order to do this, a FDM code for the weakly compressible Navier-Stokes equations has been developed. This ensures that the same physics are solved when comparing FDMs and LBMs. The spatial discretization of fluxes is carried out via central differences, which are stabilized for the advection and divergence terms. The temporal discretization is via low-storage explicit Runge-Kutta schemes. The FDM code was then ported to the GPU using the automatic FORTRAN to CUDA translator F2CUDA and optimized. Comparisons with the open source LBM solver OpenLB show that the FDM method is faster. This would seem to indicate that FDMs can compete with LBMs for the same low Mach-Number realm.