Parallel computation of unsteady incompressible viscous flows using an unstructured multigrid method

The development and validation of a parallel unstructured non-nested multigrid method for simulation of unsteady incompressible viscous flow is presented. The Navier-Stokes solver is based on the artificial compressibility method (ACM) [10] and a higher-order characteristics-based finite-volume scheme [8] on unstructured multigrids. Unsteady flow is calculated with an implicit dual time stepping scheme. The parallelization of the solver is achieved by a multigrid domain decomposition approach (MG-DD), using the Single Program Multiple Data (SPMD) programming paradigm and Message-Passing Interface (MPI) for communication of data. The parallel codes using single grids and multigrids are used to simulate steady and unsteady incompressible viscous flows over a circular cylinder for validation and performance evaluation purposes. Speedups and parallel efficiencies obtained by both the parallel single-grid and multigrid solvers are reasonably good for both test cases, using up to 32 processors on the SGI Origin 2000. A maximum speedup of 12 could be achieved on 16 processors for the unsteady flow. The parallel results obtained agree well with those of serial solvers and with numerical solutions obtained by other researchers, as well as experimental measurements.