Numerical studies of a class of reaction-diffusion equations with Stefan conditions

Title
Numerical studies of a class of reaction-diffusion equations with Stefan conditions
Publication Date
2020
Author(s)
Liu, Shuang
Du, Yihong
( author )
OrcID: https://orcid.org/0000-0002-1235-0636
Email: ydu@une.edu.au
UNE Id une-id:ydu
Liu, Xinfeng
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Taylor & Francis
Place of publication
United Kingdom
DOI
10.1080/00207160.2019.1599868
UNE publication id
une:1959.11/28559
Abstract
It is always very difficult to efficiently and accurately solve a system of differential equations coupled with moving free boundaries, while such a system has been widely applied to describe many physical/biological phenomena such as the dynamics of spreading population. The main purpose of this paper is to introduce efficient numerical methods within a general framework for solving such systems with moving free boundaries. The major numerical challenge is to track the moving free boundaries, especially for high spatial dimensions. To overcome this, a front tracking framework coupled with implicit solver is first introduced for the 2D model with radial symmetry. For the general 2D model, a level set approach is employed to more efficiently treat complicated topological changes. The accuracy and order of convergence for the proposed methods are discussed, and the numerical simulations agree well with theoretical results.
Link
Citation
International Journal of Computer Mathematics, 97(5), p. 959-979
ISSN
1029-0265
0020-7160
1026-7425
Pubmed ID
31736413
Start page
959
End page
979

Files:

NameSizeformatDescriptionLink