A new composite scheme for two-layer shallow water flows with shocks

Benkhaldoun, F.; Izem, N.; Sahmim, S.; Seaid, M.; Wakrim, M.

Abstract

This paper is devoted to solve the system of partial differential equations governing the flow of two superposed immiscible layers of shallow water flows. The system contains source terms due to bottom topography, wind stresses, and nonconservative products describing momentum exchange between the layers. The presence of these terms in the flow model forms a nonconservative system which is only conditionally hyperbolic. In addition, two-layer shallow water flows are often accompanied with moving discontinuities and shocks. Developing stable numerical methods for this class of problems presents a challenge in the field of computational hydraulics. To overcome these difficulties, a new composite scheme is proposed. The scheme consists of a time-splitting operator where in the first step the homogeneous system of the governing equations is solved using an approximate Riemann solver. In the second step a finite volume method is used to update the solution. To remove the non-physical oscillations in the vicinity of shocks a nonlinear filter is applied. The method is well-balanced, non-oscillatory and it is suitable for both low and high values of the density ratio between the two layers. Several standard test examples for two-layer shallow water flows are used to verify high accuracy and good resolution properties for smooth and discontinuous solutions.

Citation

Benkhaldoun, F., Izem, N., Sahmim, S., Seaid, M., & Wakrim, M. (2014). A new composite scheme for two-layer shallow water flows with shocks. Journal of Applied Mathematics and Computing, 44(1-2), 467-489. https://doi.org/10.1007/s12190-013-0703-z

• Journal Article Type: Article
• Publication Date: Feb 1, 2014
• Deposit Date: Jun 2, 2014
• Publicly Available Date: Jun 3, 2014
• Journal: Journal of Applied Mathematics and Computing
• Print ISSN: 1598-5865
• Electronic ISSN: 1865-2085
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 44
• Issue: 1-2
• Pages: 467-489
• DOI: https://doi.org/10.1007/s12190-013-0703-z
• Public URL: https://durham-repository.worktribe.com/output/1430103