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FEEC discretizations SIGNED

Structure-preserving discretization of hierarchically-structured rotating covariant shallow-water equations using finite element exterior calculus

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Project "FEEC discretizations" data sheet

The following table provides information about the project.

Coordinator
IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE 

Organization address
address: SOUTH KENSINGTON CAMPUS EXHIBITION ROAD
city: LONDON
postcode: SW7 2AZ
website: http://www.imperial.ac.uk/

contact info
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 Coordinator Country United Kingdom [UK]
 Project website http://www.imperial.ac.uk/ammp/research/
 Total cost 183˙454 €
 EC max contribution 183˙454 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2014
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2016
 Duration (year-month-day) from 2016-04-01   to  2018-03-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE UK (LONDON) coordinator 183˙454.00

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 Project objective

Accurate and reliable simulations of weather, ocean and climate require computational models that result from structure-preserving – e.g. mass or energy conserving – discretizations of the equations of geophysical fluid dynamics (GFD). This research project aims to derive, implement and evaluate various structure-preserving discretizations (of different order of accuracy) of the nonlinear shallow-water equations, which are suitable for weather/ocean/climate applications. The derivations will rely on a novel form of covariant equations of GFD that I have formulated using Differential Geometry, in which the equations are split into metric-free (topological) and metric-dependent parts. Based on the systematic discretization I have introduced for the split linear shallow-water equations, this project intends to extend this approach also to the split nonlinear case and to derive structure-preserving discretizations that preserve in the discrete case, too, the splitting into topological and metric terms. As the topological terms require less mathematical structure, we expect an advantage in terms of easiness of discretization and efficiency of implementation. To derive corresponding discrete equations, we apply finite element exterior calculus (FEEC) as recently Cotter and Thuburn, whose resulting discretizations of conventional covariant nonlinear shallow-water equations fulfil many desirable properties for geophysical applications. Moreover, compared to the split form I proposed, their discrete equations show a similar, however not identical, structure. We study the differences and use their derivations as guideline for ours. To implement and test the various models, we use the software libraries Firedrake and FEniCS. Besides a general “discretization recipe” to derive structure-preserving models, this project will provide open-source software which will be of practical use for the geophysical model community.

 Publications

year authors and title journal last update
List of publications.
2018 Werner Bauer, Jörn Behrens
A structure-preserving split finite element discretization of the split wave equations
published pages: 375-400, ISSN: 0096-3003, DOI: 10.1016/j.amc.2017.12.035
Applied Mathematics and Computation 325 2019-06-13
2017 Werner Bauer, François Gay-Balmaz
Variational integrators for anelastic and pseudo-incompressible flows
published pages: , ISSN: , DOI:
arXiv.org 2019-06-13
2018 Werner Bauer, Colin J Cotter
Energy-enstrophy conserving compatible finite element schemes for the shallow water equations on rotating domains with boundaries
published pages: , ISSN: , DOI:
arXiv.org 2019-06-13
2017 Werner Bauer, François Gay-Balmaz
Towards a geometric variational discretization of compressible fluids: the rotating shallow water equations
published pages: , ISSN: , DOI:
arXiv.org 2019-06-13

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