Scalable, parallel poisson polvers for CFD problems

PhD ceremony: Mr. M. Younas, 11.00 uur, Academiegebouw, Broerstraat 5, Groningen

Dissertation: Scalable, parallel poisson polvers for CFD problems

Promotor(s): prof. A.E.P. Veldman, prof. H.L. Trentelman

Faculty: Mathematics and Natural Sciences

Most of the computational resources needed to compute incompressible turbulent flow are used to solve the Poisson equation for the pressure. Therefore we have considered the parallel performance of the most efficient and scalable solvers given in PETSc (Portable, Extensible Toolkit for Scientific Computation) for linear systems, e.g. Krylov Subspace Methods and Algebraic Multigrid methods.

The symmetric Poisson problem in three dimensions with up to 1000 Million grid points has been solved. The CG method with ML as preconditioner gives the best results. In case the boundary conditions yield a non-symmetric Poisson matrix, the problem has been solved with the help of GMRES in combination with various preconditioners. In non-symmetric Poisson case the problems are evolved after the discretization of Navier-Stokes equations (conservation of mass and momentum) for incompressible one-phase and compressible two-phase flow, following a free water surface with in- and outflow boundary conditions. Also in this case an AMG preconditioner shows good results. Furthermore, the direct numerical simulations of turbulent channel ows are considered for a series of Reynolds numbers up to Re approximately 1400. For that up to 1024 processors are used. The Poisson solver for the pressure is again taken from the PETSc toolkit, and the Message Passing Interface (MPI) standard is applied to transform the re- maining parts of the computer program into a parallel Fortran-code. The Poisson solver takes about 90% of the computing time. The computations are performed at Huygens, Amsterdam. In this application the ML preconditioner turns out to be slightly more efficient than BoomerAMG.