<abstract xmlns="http://www.w3.org/1999/xhtml"><p> As an extension of a previous work considering a fully advective formulation on Cartesian meshes, a mass conservative discretization approach is presented here for the shallow water equations, based on discontinuous finite elements on general structured meshes of quadrilaterals. A semi-implicit time integration is performed by employing the TR-BDF<sub>2</sub> scheme and is combined with the semi-Lagrangian technique for the momentum equation only. Indeed, in order to simplify the derivation of the discrete linear Helmoltz equation to be solved at each time-step, a non-conservative formulation of the momentum equation is employed. The Eulerian flux form is considered instead for the continuity equation in order to ensure mass conservation. Numerical results show that on distorted meshes and for relatively high polynomial degrees, the proposed numerical method fully conserves mass and presents a higher level of accuracy than a standard off-centered Crank Nicolson approach. This is achieved without any significant imprinting of the mesh distortion on the solution.</p></abstract>

As an extension of a previous work considering a fully advective formulation on Cartesian meshes, a mass conservative discretization approach is presented here for the shallow water equations, based on discontinuous finite elements on general structured meshes of quadrilaterals. A semi-implicit time integration is performed by employing the TR-BDF2 scheme and is combined with the semi-Lagrangian technique for the momentum equation only. Indeed, in order to simplify the derivation of the discrete linear Helmoltz equation to be solved at each time-step, a non-conservative formulation of the momentum equation is employed. The Eulerian flux form is considered instead for the continuity equation in order to ensure mass conservation. Numerical results show that on distorted meshes and for relatively high polynomial degrees, the proposed numerical method fully conserves mass and presents a higher level of accuracy than a standard off-centered Crank Nicolson approach. This is achieved without any significant imprinting of the mesh distortion on the solution.

A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals

Earth System Physics Section, The Abdus Salam International Centre for Theoretical Physics, Trieste,

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

As an extension of a previous work considering a fully advective formulation on Cartesian meshes, a mass conservative discretization approach is presented here...

A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals

Published Online: Oct 01, 2016

Page range: 165 - 190

Received: Jun 12, 2015

Accepted: Jul 29, 2015

DOI: https://doi.org/10.1515/caim-2016-0026

Keywords
discontinuous Galerkin methods, semi-implicit discretizations, semi-Lagrangian discretizations, shallow water equations, qudrilateral meshes

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals

Published Online: Oct 01, 2016

Page range: 165 - 190

Received: Jun 12, 2015

Accepted: Jul 29, 2015

DOI: https://doi.org/10.1515/caim-2016-0026

Keywordsdiscontinuous Galerkin methods, semi-implicit discretizations, semi-Lagrangian discretizations, shallow water equations, qudrilateral meshes

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
discontinuous Galerkin methods, semi-implicit discretizations, semi-Lagrangian discretizations, shallow water equations, qudrilateral meshes