A multigrid solver for the incompressible Navier-Stokes equations on a Beowulf-class system

This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a solid obstacle. From a numerical point of view, the main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform we have used Coral, a Beowulf-class system based on a high performance GigaNet cLAN interconnect and Dual Pentium III nodes. The solver which has been devised taking both algorithmic and architectural issues into account, not only attains good convergence rates, but also achieves satisfactory efficiencies on the target cluster.