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A Well-Balanced Wet–Dry Front Reconstruction for Two-Layer Shallow Water Flows

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  • Xue Wang

    (School of Applied Sciences, Taiyuan University of Science and Technology, Taiyuan 030024, China
    School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China)

Abstract

In this paper, a well-balanced and positivity-preserving scheme for the nonconservative two-layer shallow water equations is developed in the framework of the finite volume method. To address the challenges posed by wet–dry fronts, the focus of our study is on reconstructing them for each layer to ensure a well-balanced property. To this end, a new numerical discretization and a special wet–dry front reconstruction are proposed. In addition, the draining time method is employed to ensure the positivity of the water depth. We prove that the proposed scheme is both well-balanced in steady-state solutions and positivity-preserving. Finally, numerical experiments demonstrate the robustness of the scheme.

Suggested Citation

  • Xue Wang, 2026. "A Well-Balanced Wet–Dry Front Reconstruction for Two-Layer Shallow Water Flows," Mathematics, MDPI, vol. 14(4), pages 1-31, February.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:4:p:595-:d:1860052
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