A FFT Preconditioning Technique for the Solution of Incompressible Flow on GPU's

MARIO A. STORTI; PAZ RODRIGO; DALCÍN LISANDRO; COSTARELLI, SANTIAGO; IDELSOHN, SERGIO

COMPUTERS & FLUIDS

PERGAMON-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2012 vol. 74 p. 44 - 57

0045-7930

Graphic processing units have received much attention in last years. Compute-intensive algorithms oper-ating on multidimensional arrays that have nearest neighbor dependency and/or exploit data locality canachieve massive speedups. Simulation of problems modeled by time-dependent Partial Differential Equa-tions by using explicit time-stepping methods on structured grids is an instance of such GPU-friendlyalgorithms. Solvers for transient incompressible fluid flow cannot be developed in a fully explicit mannerdue to the incompressibility constraint. Segregated algorithms like the fractional step method require thesolution of a Poisson problem for the pressure field at each time level. This stage is usually the most time-consuming one. This work discuss a solver for the pressure problem in applications using immersedboundary techniques in order to account for moving solid bodies. This solver is based on standard Con-jugate Gradients iterations and depends on the availability of a fast Poisson solver on the whole domainto define a preconditioner. We provide a theoretical and numerical evidence on the advantages of ourapproach versus classical techniques based on fixed point iterations such as the Iterated Orthogonal Pro-jection method.