GPGPU in Real Time CFD. Preliminary report

MARIO A. STORTI; RODRIGO R. PAZ; LISANDRO D. DALCÍN

2009-12-01/2010-12-31

1-20

Informática (software)

Ciencia y cultura-Ciencia y tecnologia

The objective of the present plan is to develop algorithms for the solution of problems in Computational Fluid Dynamics using General Purpose Graphics Processing Units (GPGPU’s).We propose to develop the following solvers:(A) An explicit FDM solver for the Poisson equation. This will serve as a first approach to programming in the GPU and also will determine which approach will be used in the solution of the Poisson stage for the Fractional Step solver. Several strategies will be examined: a) Richardson iteration, b) Preconditioned Conjugate Gradient (PCG), and c) CG with Geometric Multigrid preconditioning.(B) An explicit Fractional Step Method for the incompressible Navier-Stokes equations with FVM discretization on a structured grid. Initially the Poisson equation will be solved with a Fast Fourier Transform (FFT) technique. This is a very efficient solver (O(n log n) for an exact solution, not iterative)but imposes some restrictions, for instance the grid sizes in each direction must be a power of two.However this solver could be replaced afterwards by the best choice found in task (A).(C) An explicit FVM solver for the shallow water and the inviscid compressible subsonic Eulerequations.