A finite-difference algorithm for multiple moving boundary problems using real and virtual grid networks
type: Item
instance of: scholarly article
title: A finite-difference algorithm for multiple moving boundary problems using real and virtual grid networks
zbMATH Open document ID: 0806.65131
author: M. Zerroukat
author: Chris R. Chatwin
published in: Journal of Computational Physics
publication date: 1995-02-09T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 80A22
zbMATH DE Number: 622261
zbMATH Keywords: finite difference algorithm
zbMATH Keywords: multiple moving boundary problems
zbMATH Keywords: virtual grid network
zbMATH Keywords: Stefan problem
zbMATH Keywords: heat transfer
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: jcph.1994.1102
OpenAlex ID: W1999857553
DOI: 10.1006/JCPH.1994.1102
description: scientific article; zbMATH DE number 622261