Simulation of soliton‐like waves generated by topography with conservative fully discrete shallow‐water arbitrary‐order schemes
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 18 September 2009
Abstract
Purpose
The purpose of this paper is to suggest a new approach to the numerical simulation of shallow‐water flows both in plane domains and on the sphere.
Design/methodology/approach
The approach involves the technique of splitting of the model operator by geometric coordinates and by physical processes. Specially chosen temporal and spatial approximations result in one‐dimensional finite difference schemes that conserve the mass and the total energy. Therefore, the mass and the total energy of the whole two‐dimensional split scheme are kept constant too.
Findings
Explicit expressions for the schemes of arbitrary approximation orders in space are given. The schemes are shown to be mass‐ and energy‐conserving, and hence absolutely stable because the square root of the total energy is the norm of the solution. The schemes of the first four approximation orders are then tested by simulating nonlinear solitary waves generated by a model topography. In the analysis, the primary attention is given to the study of the time‐space structure of the numerical solutions.
Originality/value
The approach can be used for the numerical simulation of shallow‐water flows in domains of both Cartesian and spherical geometries, providing the solution adequate from the physical and mathematical standpoints in the sense of keeping its mass and total energy constant even when fully discrete shallow‐water models are applied.
Keywords
Citation
Skiba, Y.N. and Filatov, D.M. (2009), "Simulation of soliton‐like waves generated by topography with conservative fully discrete shallow‐water arbitrary‐order schemes", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 19 No. 8, pp. 982-1007. https://doi.org/10.1108/09615530910994469
Publisher
:Emerald Group Publishing Limited
Copyright © 2009, Emerald Group Publishing Limited