NPAC Technical Report SCCS-739
Parallel Multigrid Computation of the Unsteady Incompressible Navier-Stokes Equations
Ammar Degani, Geoffrey Fox
Submitted September 15 1995
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 not only necessary 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 (FAS) 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 (SPMD) 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.