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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 1, Pages 149–163 (Mi zvmmf9981)  

This article is cited in 4 scientific papers (total in 4 papers)

Analytical and numerical Riemann solutions of the Saint Venant equations for forward- and backward-facing step flows

O. V. Bulatov

Faculty of Physics, Moscow State University, Moscow, 119992, Russia

Abstract: Analytical solutions of the Saint Venant equations for five typical Riemann problems over a forward- or backward-facing step are constructed. These analytical solutions are used as reference ones to estimate the accuracy of simulated discontinuous solutions based on the regularized shallow water equations.

Key words: Saint Venant equation, Riemann problem, shallow water equations, finite difference method.

DOI: https://doi.org/10.7868/S0044466914010049

Full text: PDF file (414 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:1, 158–171

Bibliographic databases:

UDC: 519.634
Received: 02.08.2013

Citation: O. V. Bulatov, “Analytical and numerical Riemann solutions of the Saint Venant equations for forward- and backward-facing step flows”, Zh. Vychisl. Mat. Mat. Fiz., 54:1 (2014), 149–163; Comput. Math. Math. Phys., 54:1 (2014), 158–171

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. V. Bulatov, T. G. Elizarova, “Regularized shallow water equations for numerical simulation of flows with a moving shoreline”, Comput. Math. Math. Phys., 56:4 (2016), 661–679  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. Zlotnik, V. Gavrilin, “On a conservative finite-difference method for 1D shallow water flows based on regularized equations”, Mathematical Problems in Meteorological Modelling, Mathematics in Industry, 24, eds. A. Batkai, P. Csomos, I. Farago, A. Horanyi, G. Szepszo, Springer Int Publishing Ag, 2016, 3–18  crossref  mathscinet  zmath  isi
    3. A. I. Aleksyuk, V. V. Belikov, “Simulation of shallow water flows with shoaling areas and bottom discontinuities”, Comput. Math. Math. Phys., 57:2 (2017), 318–339  mathnet  crossref  crossref  isi  elib
    4. Aleksyuk I A. Belikov V.V., “The Uniqueness of the Exact Solution of the Riemann Problem For the Shallow Water Equations With Discontinuous Bottom”, J. Comput. Phys., 390 (2019), 232–248  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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