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Simulation of shallow water flows with shoaling areas and bottom discontinuities

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Abstract

A numerical method based on a second-order accurate Godunov-type scheme is described for solving the shallow water equations on unstructured triangular-quadrilateral meshes. The bottom surface is represented by a piecewise linear approximation with discontinuities, and a new approximate Riemann solver is used to treat the bottom jump. Flows with a dry sloping bottom are computed using a simplified method that admits negative depths and preserves the liquid mass and the equilibrium state. The accuracy and performance of the approach proposed for shallow water flow simulation are illustrated by computing one- and two-dimensional problems.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    A. I. Aleksyuk

  2. Water Problems Institute, Russian Academy of Sciences, Moscow, 119333, Russia

    A. I. Aleksyuk & V. V. Belikov

Authors
  1. A. I. Aleksyuk
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  2. V. V. Belikov
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Correspondence to A. I. Aleksyuk.

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Original Russian Text © A.I. Aleksyuk, V.V. Belikov, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 2, pp. 316–338.

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Aleksyuk, A.I., Belikov, V.V. Simulation of shallow water flows with shoaling areas and bottom discontinuities. Comput. Math. and Math. Phys. 57, 318–339 (2017). https://doi.org/10.1134/S0965542517020026

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  • DOI: https://doi.org/10.1134/S0965542517020026

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