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A multigrid scheme is proposed for the pressure equation of theincompressible unsteady fluid flow equations, allowing efficient implementationon clusters of modern CPUs, many integrated core devices (MICs), and graphicsprocessing units (GPUs). It is shown that the total number of thesynchronization events can be significantly reduced when a deep, 2h gridhierarchy 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. Inaddition, optimal memory transfer is also ensured, since no strided memoryaccess is required. We report increasing arithmetic intensity of the smoothingsteps when compared to the conventional additive correction multigrid (ACM),however it is counterbalanced in runtime by the decreasing number of theexpensive restriction steps. A systematic construction methodology for thecoarse grid stencil is also presented that helps in moderating the excessarithmetic intensity associated with the aggressive coarsening. Our higherorder interpolated stencil improves convergence rate via minimizing spuriousinterference between the coarse and the fine scale solutions. The method isdemonstrated on solving the pressure equation for 2D incompressible fluid flow:The benchmark setups cover shear driven laminar flow in cavity, and directnumerical simulation (DNS) of a turbulent jet. We have compared our scheme tothe ACM in terms of the arithmetic intensity of the iterations and the numberof the synchronization calls required. Also the strong scaling is plotted forour scheme when using a hybrid OpenCl/MPI based parallelization.

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