Petascale DNS using the fast Poisson solver PSH3D

Abstract eng:
Direct numerical simulation (DNS) of high Reynolds number (Re = O(105 )) turbulent flows requires computational meshes of O(1012 ) grid points. Thus, DNS requires the use of petascale supercomputers. DNS often requires the solution of a Helmholtz (or Poisson) equation for pressure, which constitutes the bottleneck of the solver. We have developed and implemented a parallel solver of the Helmholtz equation in 3D called petascale Helmholtz 3D (PSH3D). The numerical method underlying PSH3D combines a parallel 2D Fast Fourier transform (P2DFFT) and a parallel linear solver (PLS). Our numerical results show that PSH3D scales up to at least 262,144 cores. PSH3D has a peak performance 6× faster than 3D FFT-based methods (e.g., P3DFFT) when used with the partial-global optimization. We have verified that the use of PSH3D with the partial-global optimization in our DNS solver does not reduce the accuracy of the numerical solution when tested for the Taylor-Green vortex flow.

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