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Monge-Ampére based moving mesh methods for numerical weather prediction, with applications to the Eady problem

Budd, C. J.; Cullen, M. J.P.; Walsh, E. J.

Authors

C. J. Budd

M. J.P. Cullen

Emily Walsh Emily3.Walsh@uwe.ac.uk
Senior Lecturer in Mathematics



Abstract

We derive a moving mesh method based upon ideas from optimal transport theory which is suited to solving PDE problems in meteorology. In particular we show how the Parabolic Monge-Ampére method for constructing a moving mesh in two-dimensions can be coupled successfully to a pressure correction method for the solution of incompressible flows with significant convection and subject to Coriolis forces. This method can be used to resolve evolving small scale features in the flow. In this paper the method is then applied to the computation of the solution to the Eady problem which is observed to develop large gradients in a finite time. The moving mesh method is shown to work and be stable, and to give significantly better resolution of the evolving singularity than a fixed, uniform mesh. © 2012 Elsevier Inc.

Citation

Budd, C. J., Cullen, M. J., & Walsh, E. J. (2013). Monge-Ampére based moving mesh methods for numerical weather prediction, with applications to the Eady problem. Journal of Computational Physics, 236(1), 247-270. https://doi.org/10.1016/j.jcp.2012.11.014

Journal Article Type Article
Publication Date Mar 1, 2013
Journal Journal of Computational Physics
Print ISSN 0021-9991
Electronic ISSN 1090-2716
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 236
Issue 1
Pages 247-270
DOI https://doi.org/10.1016/j.jcp.2012.11.014
Keywords moving mesh method, Monge Ampére, numerical weather prediction, Eady problem
Public URL https://uwe-repository.worktribe.com/output/933979
Publisher URL http://dx.doi.org/10.1016/j.jcp.2012.11.014