APPLICATION OF BLOCK-IMPLICIT MULTIGRID APPROACH TO THREE-DIMENSIONAL HEAT TRANSFER PROBLEMS INVOLVING DISCRETE HEATING

Abstract

In this study, the performance of the symmetrically coupled Gauss-Seidel (SCGS) based multigrid method was investigated by applying it to three-dimensional conjugate heat transfer in two different configurations with discrete heat sources. These include a natural convection cooled rectangular enclosure with a discrete heat source mounted on one vertical wall, and a mixed forced convection cooled channel with a discrete heat source on the bottom wall. The convergence rates using the semi-implicit method for pressure-linked equations revised (SIMPLER), SCGS, and multigrid SCGS (MG-SCGS) were compared for both configurations. The performance of MG-SCGS was tested for variations in Rayleigh number, Reynolds number, and boundary conditions. It is shown that faster convergence can be achieved by applying the multigrid technique with only two grid levels. With MG-SCGS, significant and consistent performance enhancement over SIMPLER and SCGS was obtained for the conjugate natural, mixed, and forced convection problems considered.