# A moving mesh finite element method for the solution of two-dimensional Stefan problems

G. Beckett, John A. Mackenzie, M.L. Robertson

Research output: Contribution to journalArticle

74 Citations (Scopus)

### Abstract

An r -adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of two-dimensional heat conduction problems with a phase change. The grid is obtained from a global mapping of the physical to the computational domain which is designed to cluster mesh points around the interface between the two phases of the material. The enthalpy equation is discretised using a semiimplicit Galerkin finite element method using linear basis functions. The moving finite element method is applied to problems where the phase front is cusp shaped and where the interface changes topology.
Language English 500-518 18 Journal of Computational Physics 168 2 10.1006/jcph.2001.6721 Published - 10 Apr 2001

### Fingerprint

mesh
Enthalpy
finite element method
enthalpy
Finite element method
cusps
Heat conduction
conductive heat transfer
topology
grids
Topology
formulations

### Keywords

• enthalpy
• phase change
• equidistribution
• stefan problem
• moving meshes
• moving finite elements

### Cite this

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title = "A moving mesh finite element method for the solution of two-dimensional Stefan problems",
abstract = "An r -adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of two-dimensional heat conduction problems with a phase change. The grid is obtained from a global mapping of the physical to the computational domain which is designed to cluster mesh points around the interface between the two phases of the material. The enthalpy equation is discretised using a semiimplicit Galerkin finite element method using linear basis functions. The moving finite element method is applied to problems where the phase front is cusp shaped and where the interface changes topology.",
keywords = "enthalpy, phase change, equidistribution, stefan problem, moving meshes, adaptive method, moving finite elements",
author = "G. Beckett and Mackenzie, {John A.} and M.L. Robertson",
year = "2001",
month = "4",
day = "10",
doi = "10.1006/jcph.2001.6721",
language = "English",
volume = "168",
pages = "500--518",
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}

A moving mesh finite element method for the solution of two-dimensional Stefan problems. / Beckett, G.; Mackenzie, John A.; Robertson, M.L.

In: Journal of Computational Physics, Vol. 168, No. 2, 10.04.2001, p. 500-518.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A moving mesh finite element method for the solution of two-dimensional Stefan problems

AU - Beckett, G.

AU - Mackenzie, John A.

AU - Robertson, M.L.

PY - 2001/4/10

Y1 - 2001/4/10

N2 - An r -adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of two-dimensional heat conduction problems with a phase change. The grid is obtained from a global mapping of the physical to the computational domain which is designed to cluster mesh points around the interface between the two phases of the material. The enthalpy equation is discretised using a semiimplicit Galerkin finite element method using linear basis functions. The moving finite element method is applied to problems where the phase front is cusp shaped and where the interface changes topology.

AB - An r -adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of two-dimensional heat conduction problems with a phase change. The grid is obtained from a global mapping of the physical to the computational domain which is designed to cluster mesh points around the interface between the two phases of the material. The enthalpy equation is discretised using a semiimplicit Galerkin finite element method using linear basis functions. The moving finite element method is applied to problems where the phase front is cusp shaped and where the interface changes topology.

KW - enthalpy

KW - phase change

KW - equidistribution

KW - stefan problem

KW - moving meshes

KW - moving finite elements

UR - http://dx.doi.org/10.1006/jcph.2001.6721

U2 - 10.1006/jcph.2001.6721

DO - 10.1006/jcph.2001.6721

M3 - Article

VL - 168

SP - 500

EP - 518

JO - Journal of Computational Physics

T2 - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

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