A Finite-Difference Algorithm for Multiple Moving Boundary Problems Using Real and Virtual Grid Networks

Abstract

Most numerical methods developed for moving boundary or Stefan problems deal with the case of a single moving boundary (MB) separating two different media. Although this is applicable to a large number of engineering problems, there are many problems where more than one MB exists simultaneously during the process. A heat transfer process involving heating of a solid, melting, and partial vaporisation of liquid can be considered as a three-phase Stefan or two MB problem, where the time of appearance and disappearance of phases are to be determined as a part of the solution. An explicit unconditionally stable numerical scheme for such problems is presented and tested herein. The approach originates from the explicit variable time step (EVTS) method, developed by the same authors, for single MB problems. During the vaporisation stage, where two MBs exist simultaneously, the method uses a virtual distorted grid network moving in parallel to the vapour/liquid interface in order to determine its position vis-à-vis the real grid network. The method has been tested by solving both the collapse of an adiabatic wall and a normalised two-MB problem whose exact solution is known.