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

• Published in: International journal of heat and mass transfer 2021-10, Vol.178, p.121569, Article 121569
• Main Authors: Nandi, Subhankar, Sanyasiraju, Y.V.S.S.
• Format: Article
• Language: English
• Subjects: ADI Splitting; Body-fitted formulation; Mixed derivative term; Moving boundary; Stefan problem; Von Neumann stability
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2021.121569

•Ease of doing computations over a structured uniform grid even for arbitrary irregular domains.•Higher dimensional computations based on an efficient Tri-diagonal solver.•No additional restriction on time step, other than the accuracy requirement, as the developed scheme is unconditionally stable.•Accurate prediction of interface boundaries for both stable and unstable problems of solidification.•Capability to handle solidification with mild surface tension and kinetic mobility 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.