Central schemes and contact discontinuities
Alexander Kurganov, Guergana Petrova (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Alexander Kurganov, Guergana Petrova (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Jorge Balbás, Smadar Karni (2009)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness...
Michael Breuss (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We discuss the occurrence of oscillations when using central schemes of the Lax-Friedrichs type (LFt), Rusanov's method and the staggered and non-staggered second order Nessyahu-Tadmor (NT) schemes. Although these schemes are monotone or TVD, respectively, oscillations may be introduced at local data extrema. The dependence of oscillatory properties on the numerical viscosity coefficient is investigated rigorously for the LFt schemes, illuminating also the properties of Rusanov's...
Manuel Castro, Jorge Macías, Carlos Parés (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The goal of this paper is to construct a first-order upwind scheme for solving the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water fluids. This is done by generalizing a numerical scheme presented by Bermúdez and Vázquez-Cendón [3, 26, 27] for solving one-layer shallow water equations, consisting in a -scheme with a suitable treatment of the source terms. The difficulty in the two layer system comes from...