The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method
type: Item
instance of: scholarly article
title: The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method
zbMATH Open document ID: 0965.65105
author: N. Delaunay
published in: Journal of Computational Physics
publication date: 2001-07-16T00:00:00Z
review text: The authors describe and analyze a new numerical method for solving the multiphase Stefan problem for a general nonlinear one-dimensional heat conduction equation. They reformulate the problem using an enthalpy function and use a semi-implicit moving mesh discretization to approximate the resulting weak formulation. The discontinuities in the enthalpy-temperature relation are smoothed as a part of this process. The mesh modification strategy allows then smooth evolution of mesh nodes to track the interfaces. The system of nonlinear algebraic equations at each time step is shown to possess a unique solution and solved by Newton's method. Numerical experiments with two examples are described in detail showing good performance of the method. No unphysical staircase behaviour of the phase interfaces (common with using fixed uniform meshes in the enthalpy formulations) is observed here. Extensions of the methodology for problems in more than one dimension are shortly discussed in the end of the paper.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 65M50
zbMATH DE Number: 1496457
zbMATH Keywords: moving boundary problem
zbMATH Keywords: nonlinear heat conduction
zbMATH Keywords: enthalpy formulation
zbMATH Keywords: multiphase Stefan problem
zbMATH Keywords: numerical experiments
zbMATH Keywords: adaptive moving mesh
zbMATH Keywords: Newton's method
zbMATH Keywords: performance
reviewed by: Petr Přikryl
MaRDI profile type: Publication
OpenAlex ID: W2037733619
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DOI: 10.1006/JCPH.2000.6511
description: scientific article; zbMATH DE number 1496457