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A Q -scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shadow water system

Manuel Castro, Jorge Macías, Carlos Parés (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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 Q -scheme with a suitable treatment of the source terms. The difficulty in the two layer system comes from the coupling...

A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system

Manuel Castro, Jorge Macías, Carlos Parés (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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, 6, 27] for solving one-layer shallow water equations, consisting in a Q-scheme with a suitable treatment of the source terms. The difficulty in the two layer system comes from the coupling...

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