Multigrid based computational procedure to predict internal flows with heat transfer

In this study, a formally third-order, finite volume, unstaggered (co-located), modified SIMPLE algorithm-based 2D code was created utilizing multigrid for fast convergence. Stone's Strongly Implicit Procedure (SIP) is employed as a relaxation (smoother, matrix eq. solver) method, due to its high performance. The quadratic formulations QUICK, mixed and UTOPIA were used to discretize the convective terms in momentum equations. Velocity and pressure coupling was addressed via modified SIMPLE algorithm. Due to the co-located nature of method, the cell face velocities are obtained via the so called momentum balancing technique introduced before. The Multigrid idea is implemented to the solution of pressure correction equation. Various ways of implementing Multigrid algorithms are discussed. An ASME benchmark case (backward facing step with heat transfer) is choosen as the problem. The so called accommodative FAS-FMG was used. Predictions show that high order convective term discretization improves the predictions, while multigrid enables about an order of magnitude CPU time savings. Results point out that the promises of both high order discretization and multigrid can be harvested for recirculating flows.