Vectorized difference schemes for a three dimensional enthalpy formulation for phase change problems

Abstract

Fully vectorized codes have been written for the CRAY X-MP implementing explicit and implicit finite difference schemes for enthalpy formulations of three dimensional Stefan-like problems. The implicit scheme is that proposed by C.M. Elliot and J.R. Ockendon. The explicit scheme is intended to provide a comparison for the results from the implicit scheme. Vectorization of the code required some ingenuity since material properties change discontinuously as solidification proceeds. Boolean variables were used to avoid conditional branches in DO loops. Average vector length was greatly increased by unfolding three dimensional arrays and treating them as long vectors. This report documents the development of the code and the vectorization strategies. The investigation of the tradeoffs between the implicit scheme, potentially capable of taking large time steps, and the explicit scheme, whose time step size is limited by the stability criterion, has begun but is not complete. 4 refs., 6 figs.