A Numerical Algorithm for the Solution of Viscous Incompressible Flow on GPU's

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

Buenos Aires

Simposio; V Latin American Symposium on High Performance Computing HPCLatAm 2012; 2012

Sociedad Argentina de Informática e Investigación Operativa

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.