Massively Parallel Solvers for Computational Fluid Dynamics on Multi-Block Cartesian Grids

Document Type

Student Presentation

Presentation Date



College of Arts and Sciences



Faculty Sponsor

Grady Wright


We describe several numerical solvers for the pressure Poisson equation arising in models of incompressible fluid flow. We employ multi-block Cartesian grids to adaptively refine the computational domain used to model the fluid flow equations. These equations are then discretized using second order finite-differences. This converts the pressure equation, an elliptic, second order partial differential equation (PDE) to a large, sparse linear system of equations.

Using a variety of well established software packages (HYPRE, Trilinos, PETSc, Zoltan, FFTW, AMGx), we either form the matrix that arises from the pressure equation explicitly, and pass the large, sparse matrix to a suitable solver, or we reduce the pressure equation to equations on interfaces of the gridded subdomains and pass a smaller, dense matrix to suitable solvers. This latter approach follows a domain decomposition strategy that amounts to solving a Schur complement system.

We show parallel performance results on Kestrel and the R2 cluster for these different solvers and for various adaptively refined grids. For Kestrel, we also show results for a GPU (graphics processing unit) version of the code, which turns out to be several times faster than the CPU version.

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