Imperial College London
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ProfessorColinCotter

Faculty of Natural Sciences, Department of Mathematics

Professor of Computational Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 3468colin.cotter

 
 
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Location

 

755Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Yamazaki:2022:10.1016/j.jcp.2022.111217,
author = {Yamazaki, H and Weller, H and Cotter, CJ and Browne, PA},
doi = {10.1016/j.jcp.2022.111217},
journal = {Journal of Computational Physics},
title = {Conservation with moving meshes over orography},
url = {http://dx.doi.org/10.1016/j.jcp.2022.111217},
volume = {461},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Adaptive meshes have the potential to improve the accuracy and efficiency of atmospheric modelling by increasing resolution where it is most needed. Mesh re-distribution, or r-adaptivity, adapts by moving the mesh without changing the connectivity. This avoids some of the challenges with h-adaptivity (adding and removing points): the solution does not need to be mapped between meshes, which can be expensive and introduces errors, and there are no load balancing problems on parallel computers. A long standing problem with both forms of adaptivity has been changes in volume of the domain as resolution changes at an uneven boundary. We propose a solution which achieves exact local conservation and maintains a uniform scalar field while the mesh changes volume as it moves over orography. This is achieved by introducing a volume correction parameter which tracks the cell volumes without using expensive conservative mapping.A finite volume solution of the advection equation over orography on moving meshes is described and results are presented demonstrating improved accuracy for cost using moving meshes. Exact local conservation and maintenance of uniform scalar fields is demonstrated and the correct mesh volume is preserved.We use optimal transport to generate meshes which are guaranteed not to tangle and are equidistributed with respect to a monitor function. This leads to a Monge-Ampère equation which is solved with a Newton solver. The superiority of the Newton solver over other techniques is demonstrated in the appendix. However the Newton solver is only efficient if it is applied to the left hand side of the Monge-Ampère equation with fixed point iterations for the right hand side.
AU  - Yamazaki,H
AU  - Weller,H
AU  - Cotter,CJ
AU  - Browne,PA
DO  - 10.1016/j.jcp.2022.111217
PY  - 2022///
SN  - 0021-9991
TI  - Conservation with moving meshes over orography
T2  - Journal of Computational Physics
UR  - http://dx.doi.org/10.1016/j.jcp.2022.111217
UR  - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000802129600006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
UR  - https://www.sciencedirect.com/science/article/pii/S0021999122002790
UR  - http://hdl.handle.net/10044/1/107760
VL  - 461
ER  -
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