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 languageEnglish
Title of host publicationMesh Generation and Adaptation
Place of PublicationCham, Switzerland
Number of pages23
ISBN (Electronic)9783030925406
ISBN (Print)9783030925390
Publication statusE-pub ahead of print - 21 Feb 2022

Publication series

NameSEMA SIMAI Springer Series
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.

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


Dive into the research topics of 'An Adaptive Conservative Moving Mesh Method'. Together they form a unique fingerprint.

Cite this