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A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries

Morales-Hernandez, Mario; Hubbard, Matthew E.; Garcia-Navarro, Pilar

Authors

Mario Morales-Hernandez

MATTHEW HUBBARD MATTHEW.HUBBARD@NOTTINGHAM.AC.UK
Professor of Computational and Applied Mathematics

Pilar Garcia-Navarro



Abstract

A 2D Large Time Step (LTS) explicit scheme on structured grids is presented in this work. It is first detailed and analysed for the 2D linear advection equation and then applied to the 2D shallow water equations. The dimensional splitting technique allows us to extend the ideas developed in the 1D case related to source terms, boundary conditions and the reduction of the time step in the presence of large discontinuities. The boundary conditions treatment as well as the wet/dry fronts in the case of the 2D shallow water equations require extra effort. The proposed scheme is tested on linear and non-linear equations and systems, with and without source terms. The numerical results are compared with those of the conventional scheme as well as with analytical solutions and experimental data.

Citation

Morales-Hernandez, M., Hubbard, M. E., & Garcia-Navarro, P. (2014). A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries. Journal of Computational Physics, 263, https://doi.org/10.1016/j.jcp.2014.01.019

Journal Article Type Article
Acceptance Date Jan 15, 2014
Online Publication Date Jan 23, 2014
Publication Date Apr 15, 2014
Deposit Date Feb 27, 2017
Publicly Available Date Feb 27, 2017
Journal Journal of Computational Physics
Print ISSN 0021-9991
Electronic ISSN 0021-9991
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 263
DOI https://doi.org/10.1016/j.jcp.2014.01.019
Keywords Large time step scheme; Wet/dry fronts; Source terms; Dimensional splitting; 2D shallow water flows
Public URL http://eprints.nottingham.ac.uk/id/eprint/40810
Publisher URL http://www.sciencedirect.com/science/article/pii/S0021999114000461
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0





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