Journal of Computational Physics
Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant
Journal of Scientific Computing
High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems
Journal of Scientific Computing
Journal of Scientific Computing
Numerical Treatment of the Loss of Hyperbolicity of the Two-Layer Shallow-Water System
Journal of Scientific Computing
Computer modeling of liquid-solid impacts
Mathematical and Computer Modelling: An International Journal
Journal of Computational Physics
Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case
Journal of Computational Physics
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This paper deals with the numerical difficulties related to the appearance of the so-called wet/dry fronts that may occur during the simulation of free-surface waves in shallow fluids and internal waves in stratified fluids composed by two shallow layers of immiscible liquids. In the one-layer case, the fluid is supposed to be governed by the shallow water equations. In the case of two layers, the system to solve is formulated under the form of two-coupled system of shallow water equations. In both cases, the discretization of the equations are performed by means of the Q-schemes of Roe upwinding the source term developed in ^[^1^,^2^] for the one-layer system, and ^[^3^] for the two-layer system. These schemes satisfy the so-called C-property: they solve exactly steady solutions corresponding to water at rest. In order to handle properly with wet/dry fronts, a numerical scheme has to verify also an extended C-property: it has to solve exactly steady solutions corresponding to water at rest including wet/dry transitions. In ^[^4^-^6^], some numerical schemes satisfying this property has been obtained. In this paper, we propose an improvement of these schemes and its extension to two-layer systems. We present some numerical results: for one-layer fluids, we compare the numerical results with some measurements corresponding to a physical model. For two-layer systems, we use the numerical scheme to perform a lock-exchange experiment, and we verify its validity by comparing the steady state reached with an approximate solution obtained by Armi and Farmer in ^[^7^,^8^] by using a simplified model.