A Compact Finite Volume Scheme for 2-D Stefan Problems and Vector/Multiprocessor Computers

Abstract

We consider both the compact finite volume and finite difference space discretizations of the Stefan problem. The resulting algebraic systems are solved by nonlinear versions of ADI and SOR. Both algorithms contain significant parallelism which is demonstrated on two vector/multiprocessing computers, the Alliant FX/40 and the Cray Y-MP. Numerical experiments indicate that the compact discretization and ADI give the best accuracy with the minimum computational cost.