Parallel Unsteady 3D MG Incompressible Flow

Abstract

The development and validation of a parallel unstructured tetrahedral non-nested multigrid method for simulation of unsteady 3D incompressible viscous flow are described in this paper. The Navier-Stokes solver is based on the artificial compressibility method (ACM) and a higher-order characteristics-based finite-volume scheme on unstructured multigrid. Unsteady flow is calculated with a matrix-free implicit dual time stepping scheme. The parallelization of the multigrid solver is achieved by multigrid domain decomposition approach (MG-DD). There are two parallelization strategies proposed in this work, the first strategy is a one-level parallelization strategy using geometric domain decomposition technique alone, the second strategy is a two-level parallelization strategy that consists of a hybrid of both geometric domain decomposition and data decomposition techniques. The Message- Passing Interface (MPI) Library is used for communication of data and loop arrays are decomposed using the OpenMP standard. The parallel codes using single grid and multigrid are used to simulate steady and unsteady incompressible viscous flows for a 3D lid-driven cavity flow and flow over a 3D circular cylinder for validation and performance evaluation purposes. The speedups and efficiencies obtained by both the parallel solvers are reasonably good for all test cases.