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A New Approach for Designing Moving-Water Equilibria Preserving Schemes for the Shallow Water Equations

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Abstract

We construct a new second-order moving-water equilibria preserving central-upwind scheme for the one-dimensional Saint-Venant system of shallow water equations. The idea is based on a reformulation of the source terms as integral in the flux function. Reconstruction of the flux variable yields then a third order equation that can be solved exactly. This procedure does not require any further modification of existing schemes. Several numerical tests are performed to verify the ability of the proposed scheme to accurately capture small perturbations of steady states.

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Acknowledgements

The work of A. Chertock was supported in part by NSF Grants DMS-1521051 and DMS-1818684. The work of Y. Cheng was supported in part by NSF Grant DMS-1521009. The work of A. Kurganov was supported in part by NSFC Grant 11771201 and NSF Grant DMS-1521009. The work of M. Herty was supported in part by DFG HE5386/13-15, the cluster of excellence DFG EXC128 “Integrative Production Technology for High-Wage Countries” and the BMBF project KinOpt.

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Authors and Affiliations

  1. Mathematics Department, Tulane University, New Orleans, LA, 70118, USA

    Yuanzhen Cheng, Alexander Kurganov & Tong Wu

  2. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Alina Chertock

  3. Department of Mathematics, RWTH Aachen University, Templergraben 55, 52056, Aachen, Germany

    Michael Herty

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

    Alexander Kurganov

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  1. Yuanzhen Cheng
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Correspondence to Alexander Kurganov.

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Cheng, Y., Chertock, A., Herty, M. et al. A New Approach for Designing Moving-Water Equilibria Preserving Schemes for the Shallow Water Equations. J Sci Comput 80, 538–554 (2019). https://doi.org/10.1007/s10915-019-00947-w

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