A grid based ADI method for the problem of two phase solidification

Abstract

This paper proposes a transformation based, unconditionally stable, Alternating Direction Implicit (ADI) scheme for solving two-phase Stefan problems of solidification in arbitrary bounded domains. The governing equations of each phase are transformed, from a complex physical domain to a fixed rectangular domain, using body-fitted coordinates. ADI method is used to solve the transformed equations of each phase separately. The unconditional stability of the proposed ADI scheme is discussed numerically using von-Neumann method. Several numerical experiments are carried out for the case of stable solidification to verify the applicability of the proposed method. An excellent agreement has been found between the numerically generated values and the exact/existing solutions. Further, the developed scheme has also been tested on the problems of unstable solidification with mild surface tension and kinetic mobility. Once again the interface location with time has been computed very accurately.