A finite-difference algorithm for multiple moving boundary problems using real and virtual grid networks
A heat transfer process involving heating of a solid, melting, and partial vaporisation of a liquid as a three-phase Stefan or a two-phase moving boundary problem is considered. The times of appearance and disappearance of phases are to be determined as a part of the solution. The explicit variable time step method adopts a fixed time-space grid network during the pre-melting stage, a variable time step grid network during the melting and vaporisation stage, and uses explicit finite difference replacements for the partial and ordinary differential equations. During the vaporisation period the method uses the approach of fixing the liquid-solid interface at a real space grid line and determines the time step iteratively. The numerical method uses a virtual distorted grid network moving in parallel to the second moving boundary (MB) and determines explicitly the second MB as well as the temperature of the liquid between the two moving boundaries. Vectorisation is an essential tool to increase performance. The stability of the scheme is automatically maintained irrespective of the mesh size. The method is tested by solving both the collapse of a solid wall due to a heat flux input at one boundary with an adiabatic condition, and a normalized two-phase MB problem, the exact analytical solution of which is known. The method achieves good accuracy.
scientific article; zbMATH DE number 622261