A GPU cluster optimized multigrid scheme for computing unsteady incompressible fluid flow

A multigrid scheme is proposed for the pressure equation of the incompressible unsteady fluid flow equations, allowing efficient implementation on clusters of modern CPUs, many integrated core devices (MICs), and graphics processing units (GPUs). It is shown that the total number of the synchronization events can be significantly reduced when a deep, 2h grid hierarchy is replaced with a two-level scheme using 16h-32h restriction, fitting to the the width of the SIMD engine of modern CPUs and GPUs. In addition, optimal memory transfer is also ensured, since no strided memory access is required. We report increasing arithmetic intensity of the smoothing steps when compared to the conventional additive correction multigrid (ACM), however it is counterbalanced in runtime by the decreasing number of the expensive restriction steps. A systematic construction methodology for the coarse grid stencil is also presented that helps in moderating the excess arithmetic intensity associated with the aggressive coarsening. Our higher order interpolated stencil improves convergence rate via minimizing spurious interference between the coarse and the fine scale solutions. The method is demonstrated on solving the pressure equation for 2D incompressible fluid flow: The benchmark setups cover shear driven laminar flow in cavity, and direct numerical simulation (DNS) of a turbulent jet. We have compared our scheme to the ACM in terms of the arithmetic intensity of the iterations and the number of the synchronization calls required. Also the strong scaling is plotted for our scheme when using a hybrid OpenCl/MPI based parallelization.