NPAC Technical Report SCCS-738

Application of Parallel Multigrid Methods to Unsteady Flow: A Performance Evaluation

Ammar Degani, Geoffrey Fox

Submitted September 15 1995


Abstract

The parallel multigrid time-accurate calculation of the unsteady incompressible Navier-Stokes equations is carried out using both explicit and implicit schemes. In the explicit solution method, a `lumped' scheme is employed at the coarsest multigrid levels where all the processors solve the same problem. On the other hand, in the implicit method, in which the equations are solved in a fully-coupled mode, a `semi-distributive' scheme is used where the effective number of active processors decreases logarithmically with each coarsening of the mesh at the coarsest levels. Both V and W cycles are implemented in the explicit method and the convergence rates and execution times are compared. It is demonstrated that good speedups are obtained for the implicit scheme and the slight degradation in parallel efficiency, relative to calculations performed on the finest grid, is dominated by increased convergence rates.


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