An Adaptive Conservative Moving Mesh Method

Simone Appella; Chris Budd; Tristan Pryer

doi:10.1007/978-3-030-92540-6_13

An Adaptive Conservative Moving Mesh Method

Simone Appella, Chris Budd, Tristan Pryer

Research output: Chapter or section in a book/report/conference proceeding › Book chapter

Abstract

We present an adaptive moving mesh strategy endowed with a mass conservation property for the numerical solution of the two-dimensional linear transport equation. We achieve this through the solution of an auxiliary moving mesh problem driven by a gradient based monitor function. The method we propose is of staggered type, hence requires an appropriate data transfer operator over different meshes. We make use of an L ² projection operator that requires the construction of a supermesh for evaluation. We summarise extensive numerical experiments aimed at testing the robustness of the method and its ability to approximate challenging numerical features.

Original language	English
Title of host publication	Mesh Generation and Adaptation
Place of Publication	Cham, Switzerland
Publisher	Springer
Pages	277-299
Number of pages	23
ISBN (Electronic)	9783030925406
ISBN (Print)	9783030925390
DOIs	https://doi.org/10.1007/978-3-030-92540-6_13
Publication status	E-pub ahead of print - 21 Feb 2022

Publication series

Name	SEMA SIMAI Springer Series
Volume	30
ISSN (Print)	2199-3041
ISSN (Electronic)	2199-305X

Bibliographical note

Funding Information:
Acknowledgments This research has been funded in part by the EPSRC through the CDT program in Statistical and Applied Mathematics at the University of Bath (EPSRC Reference: EP/L015684/1). We thank the MET Office staff and the reviewer of this manuscript for their valuable advice and comments.

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Funding

This research has been funded in part by the EPSRC through the CDT program in Statistical and Applied Mathematics at the University of Bath (EPSRC Reference: EP/L015684/1). We thank the MET Office staff and the reviewer of this manuscript for their valuable advice and comments.

ASJC Scopus subject areas

Computational Mechanics
Numerical Analysis
Agricultural and Biological Sciences (miscellaneous)
Physics and Astronomy (miscellaneous)
Fluid Flow and Transfer Processes
Computational Mathematics
Industrial and Manufacturing Engineering
Applied Mathematics

Access to Document

10.1007/978-3-030-92540-6_13

Cite this

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AU - Budd, Chris

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N1 - Funding Information: Acknowledgments This research has been funded in part by the EPSRC through the CDT program in Statistical and Applied Mathematics at the University of Bath (EPSRC Reference: EP/L015684/1). We thank the MET Office staff and the reviewer of this manuscript for their valuable advice and comments. Publisher Copyright: © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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N2 - We present an adaptive moving mesh strategy endowed with a mass conservation property for the numerical solution of the two-dimensional linear transport equation. We achieve this through the solution of an auxiliary moving mesh problem driven by a gradient based monitor function. The method we propose is of staggered type, hence requires an appropriate data transfer operator over different meshes. We make use of an L 2 projection operator that requires the construction of a supermesh for evaluation. We summarise extensive numerical experiments aimed at testing the robustness of the method and its ability to approximate challenging numerical features.

AB - We present an adaptive moving mesh strategy endowed with a mass conservation property for the numerical solution of the two-dimensional linear transport equation. We achieve this through the solution of an auxiliary moving mesh problem driven by a gradient based monitor function. The method we propose is of staggered type, hence requires an appropriate data transfer operator over different meshes. We make use of an L 2 projection operator that requires the construction of a supermesh for evaluation. We summarise extensive numerical experiments aimed at testing the robustness of the method and its ability to approximate challenging numerical features.

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ER -

An Adaptive Conservative Moving Mesh Method

Abstract

Publication series

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

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Programme Grant: Mathematics of Deep Learning

Cite this

An Adaptive Conservative Moving Mesh Method

Abstract

Publication series

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Programme Grant: Mathematics of Deep Learning

Cite this