From extruded-2D to fully-3D geometries for DNS: a Multigrid-based extension of the Poisson solver
Direct numerical simulation (DNS) of incompressible flows is an essential tool for improving the understanding of the physics of turbulence and for the development of better turbulence models. The Poisson equation, the main bottleneck from a parallel point of view, usually also limits its applicability for complex geometries. In this context, efficient and scalable Poisson solvers on fully-3D geometries are of high interest.In our previous work, a scalable algorithm for Poisson equation was proposed. It performed well on both small clusters with poor network performance and supercomputers using efficiently up to a thousand of CPUs. This algorithm named Krylov-Schur-Fourier Decomposition (KSFD) can be used for problems in parallelepipedic 3D domains with structured meshes and obstacles can be placed inside the flow. However, since a FFT decomposition is applied in one direction, mesh is restricted to be uniform and obstacles to be 2D shapes extruded along this direction.The present work is devoted to extend the previous KSFD algorithm to eliminate these limitations. The extension is based on a two-level Multigrid (MG) method that uses KSFD as a solver for second level. The algorithm is applied for a DNS of a turbulent flow in a channel with wall-mounted cube. Illustrative results at Re τ = 590 (based on the cube height and the bulk velocity Re h = 7235) are shown.
Key wordsparallel 3D Poisson solver Schur complement method FFT Multigrid Preconditioned Conjugate Gradient Wall-mounted cube DNS
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