ADAPTIVE PARALLEL MULTIGRID SOLUTION OF 2D INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

In this paper an adaptive parallel multigrid method and an application example for the 2D incompressible Navier-Stokes equations are describ ed. The strategy of the adaptivity in the sense of local grid refineme nt in the multigrid context is the multilevel adaptive technique (MLAT ) suggested by Brandt. The parallelization of this method on scalable parallel systems is based on the portable communication library CLIC a nd the message-passing standards: PARMACS, PVM and MPI. The specific p roblem considered in this work is a two-dimensional hole pressure prob lem in which a Poiseuille channel flow is disturbed by a cavity on one side of the channel. Near geometric singularities a very fine grid is needed for obtaining an accurate solution of the pressure value. Two important issues of the efficiency of adaptive parallel multigrid algo rithms, namely the data redistribution strategy and the refinement cri terion, are discussed here. For approximate dynamic load balancing, ne w data in the adaptive steps are redistributed into distributed memori es in different processors of the parallel system by block remapping. Among several refinement criteria tested in this work, the most suitab le one for the specific problem is that based on finite-element residu als from the point of view of self-adaptivity and computational effici ency, since it is a kind of error indicator and can stop refinement al gorithms in a natural way for a given tolerance. Comparisons between d ifferent global grids without and with local refinement have shown the advantages of the self-adaptive technique, as this can save computer memory and speed up the computing time several times without impairing the numerical accuracy. (C) 1997 By John Wiley & Sons, Ltd.