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

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: 1090-2716
• 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: https://nottingham-repository.worktribe.com/output/727014
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0021999114000461
• Contract Date: Feb 27, 2017