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A well-balanced numerical model for depth-averaged two-layer shallow water flows

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Abstract

In this study, a well-balanced and positivity-preserving scheme for the nonconservative two-layer shallow water equations is developed in the framework of the path-conservative finite volume method. Special attention is paid to guaranteeing the well-balanced properties even in the presence of the wet–dry fronts for each layer. To this end, in this study, new numerical discretization and special local reconstruction are proposed. Moreover, the developed scheme also allows to stably compute flows in under-resolved meshes. The results of the numerical experiments illustrate the robustness and good performance of the constructed numerical scheme.

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Authors and Affiliations

  1. Numerical Environmental Prediction Section Environment and Climate Change Canada, Dorval, QC, H9P 1J3, Canada

    Xin Liu

  2. Department of Civil Engineering, University of Ottawa, Ottawa, ON, K1N 6N5, Canada

    Xin Liu

  3. College of Big Data and Internet, Shenzhen Technology University, Shenzhen, 518118, China

    Junfeng He

Authors
  1. Xin Liu
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  2. Junfeng He
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Correspondence to Junfeng He.

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Communicated by Cassio Oishi.

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Liu, X., He, J. A well-balanced numerical model for depth-averaged two-layer shallow water flows. Comp. Appl. Math. 40, 311 (2021). https://doi.org/10.1007/s40314-021-01698-x

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  • DOI: https://doi.org/10.1007/s40314-021-01698-x

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