Parallel Multigrid Computation of the Unsteady Incompressible Navier–Stokes Equations

Abstract

Parallel computation on distributed-memory machines offers the capability of a scalable approach to the solution of large CFD problems. However, in order to fully realize this capability, it is necessary not only to devise parallel methodologies, but also to develop numerical schemes for which the computational effort also scales with problem size. To this end, a parallel multigrid scheme for the calculation of the unsteady incompressible Navier–Stokes equations is considered here. A spatial and temporal second-order accurate implicit discretization scheme on a staggered grid is employed, and a full approximation storage multigrid method, appropriate for nonlinear problems, is used. A parallel solver is developed which smooths the equations at each multigrid level in a fully coupled mode. The programming paradigm is single program multiple data with message passing. In comparison with single-grid calculations, it is demonstrated that the convergence rate for multigrid calculations is considerably superior and dominates the slight degradation in speed up.