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A large time-step implicit moving mesh scheme for moving boundary problems

Baines, M. J. and Lee, T. E. (2014) A large time-step implicit moving mesh scheme for moving boundary problems. Numerical Methods for Partial Differential Equations, 30 (1). pp. 321-338. ISSN 1098-2426

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To link to this item DOI: 10.1002/num.21812

Abstract/Summary

Velocity-based moving mesh methods update the mesh at each time level by using a velocity equation with a time-stepping scheme. A particular velocity-based moving mesh method, based on conservation, uses explicit time-stepping schemes with small time steps to avoid mesh tangling. However, this can prove to be impractical when long-term behavior of the solution is of interest. Here, we present a semi-implicit time-stepping scheme which manipulates the structure of the velocity equation such that it resembles a variable-coefficient heat equation. This enables the use of maximum/minimum principle which ensures that mesh tangling is avoided. It is also shown that this semi-implicit scheme can be extended to a fully implicit time-stepping scheme. Thus, the time-step restriction imposed by explicit schemes is overcome without sacrificing mesh structure.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:68030
Publisher:Wiley

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