<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.</p></abstract>

We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.

The semi-Lagrangian method on curvilinear grids

Max Planck Institute for plasma physics, Garching b. München,

Mathematics center, TU Munich, Garching b. München,

Communications in Applied and Industrial Mathematics

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

{"article-title":"The semi-Lagrangian method on curvilinear grids"}

We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass...

The semi-Lagrangian method on curvilinear grids

Pubblicato online: 01 ott 2016

Pagine: 99 - 137

Ricevuto: 15 mag 2015

Accettato: 13 nov 2015

DOI: https://doi.org/10.1515/caim-2016-0024

Parole chiave
Vlasov equation, guiding center model, semi-Lagrangian method, curvilinear grid, mapped grid

© 2016

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

The semi-Lagrangian method on curvilinear grids

Pubblicato online: 01 ott 2016

Pagine: 99 - 137

Ricevuto: 15 mag 2015

Accettato: 13 nov 2015

DOI: https://doi.org/10.1515/caim-2016-0024

Parole chiaveVlasov equation, guiding center model, semi-Lagrangian method, curvilinear grid, mapped grid

© 2016

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

Parole chiave
Vlasov equation, guiding center model, semi-Lagrangian method, curvilinear grid, mapped grid