Optimized GPU based simulation of the incompressible Navier-Stokes equations on a MAC grid

The paper introduces an optimized GPU based implementation of the incompressible Navier-Stokes equations which are solved using the artificial compressibility method. The numerical scheme is based on a finite difference method. The domain on which the simulations have been performed is a backward facing step problem and the discretizations have been carried out on a MAC grid. The most time consuming parts, i.e. the computations of the velocities and of the pressure values, have been moved onto the GPU. Two separate kernels have been defined because there is no communication between the blocks of the GPU grid. Several optimization strategies have incrementally increased the performance of the two kernels. The most important ones are: coalesced global memory, reduced read and copy operations and optimum usage of shared memory. The results of the comparison between the CPU and GPU performance indicate a speed-up which varies from just under one order of magnitude for the coarsest grid up to two orders of magnitude for the finest grid.