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Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Models

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Abstract

We extend recently proposed flux globalization based well-balanced path-conservative central-upwind schemes to several shallow water models including the Saint-Vevant system with and without the Manning friction term and rotating shallow water equations. We focus on development of the well-balanced schemes capable of exactly preserving quite complicated steady-state solutions the studied systems admit when the bottom topography is discontinuous. In such cases, nonconservative product terms naturally appear and they require a special treatment. To this end, we incorporate the nonconservative product terms into the global fluxes using the path-conservative technique implemented within a framework of simple—yet highly accurate and robust—Riemann-problem-solver-free central-upwind schemes. This results in new flux globalization based central-upwind schemes, which are more accurate than their existing counterparts. The advantages of the proposed schemes are demonstrated on a number of numerical examples.

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Data and Software Availability

The data that support the findings of this study and FORTRAN codes developed by the authors and used to obtain all of the presented numerical results are available from the corresponding author upon reasonable request.

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Funding

The work of A. Kurganov was supported in part by NSFC grants 12171226 and 12111530004, and by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design (No. 2019B030301001).

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Authors and Affiliations

  1. Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China

    Yangyang Cao, Yongle Liu & Ruixiao Xin

  2. Department of Mathematics, SUSTech International Center for Mathematics and Guangdong Provincial Key Laboratory of Computational Science and Material Design, Southern University of Science and Technology, Shenzhen, 518055, China

    Alexander Kurganov

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  1. Yangyang Cao
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Correspondence to Yongle Liu.

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Cao, Y., Kurganov, A., Liu, Y. et al. Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Models. J Sci Comput 92, 69 (2022). https://doi.org/10.1007/s10915-022-01912-w

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