Application of parallel multigrid methods to unsteady flow: A performance evaluation

Abstract

This chapter describes the parallel multi-grid time-accurate calculation of the unsteady incompressible Navier-Stokes equations by using both explicit and implicit schemes. In the explicit solution method, a lumped scheme is employed at the coarsest multi-grid levels where all the processors solve the same problem. 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. The primary objective is the evaluation of parallel multigrid methods to unsteady flow in terms of convergence rates and parallel efficiency as the size of the problem and number of processors is varied. Both “V” and “W” cycles are implemented in the explicit method and the convergence rates and execution times are compared. The chapter demonstrates 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.