Parallel Multigrid Computation of the Unsteady Incompressible Navier–Stokes Equations

✍ Scribed by A.T. Degani; G.C. Fox

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 536 KB
• Volume: 128
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0205

✦ Synopsis

ment is satisfied but not the second, is in the solution of the two-dimensional Poisson equation using the Gauss-Seidel Parallel computation on distributed-memory machines offers the capability of a scalable approach to the solution of large CFD prob-method. With a red-black ordering scheme and a block lems. However, in order to fully realize this capability, it is necessary distribution of data, the parallel implementation of the not only to devise parallel methodologies, but also to develop nu-Gauss-Seidel method is known to be scalable [1]; however, merical schemes for which the computational effort also scales the computational effort required to obtain a converged with problem size. To this end, a parallel multigrid scheme for the solution is of O(N 2 log N ) which makes this numerical calculation of the unsteady incompressible Navier-Stokes equations is considered here. A spatial and temporal second-order accu-scheme impractical for large problems. Thus, it is mainrate implicit discretization scheme on a staggered grid is employed, tained that the two most desirable features of computaand a full approximation storage multigrid method, appropriate for tional algorithms for large problems, typical of those in nonlinear problems, is used. A parallel solver is developed which CFD, are: (i) the computational effort required by the smooths the equations at each multigrid level in a fully coupled numerical scheme to solve a problem of size N is, say, no mode. The programming paradigm is single program multiple data with message passing. In comparison with single-grid calculations, more than O(N log N ), and (ii) the parallel implementation it is demonstrated that the convergence rate for multigrid calculaof the numerical scheme is scalable with the number of tions is considerably superior and dominates the slight degradation processors p for N/p large and fixed.