This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys. 102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...

This paper is concerned with the numerical approximations of Cauchy problems for
one-dimensional nonconservative hyperbolic systems.
The first goal is to introduce a general concept of well-balancing
for numerical schemes solving this kind of systems. Once this concept stated, we
investigate the well-balance properties of numerical schemes based on the
generalized Roe linearizations introduced by [Toumi,
(1992) 360–373]. Next, this general theory
is applied to obtain well-balanced...

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...

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

The goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a turbidity current model. The main difficulties come from the nonconservative nature of the system. A general strategy to derive simple approximate Riemann solvers for nonconservative systems is introduced, which is applied to the turbidity current model to obtain two different HLLC solvers. Some results concerning the non-negativity...

The goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type
approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a
turbidity current model. The main difficulties come from the nonconservative nature of the
system. A general strategy to derive simple approximate Riemann solvers for
nonconservative systems is introduced, which is applied to the turbidity current model to
obtain two different...

Presentamos un modelo numérico unidimensional para flujos bicapa que se ha desarrollado para la simulación de flujos a través de canales con geometría irregular tanto en anchura como en profundidad. Este modelo se utiliza para el estudio y simulación de las mareas internas que tienen lugar en el Estrecho de Gibraltar. En primer lugar presentaremos las ecuaciones del modelo y el esquema numérico que se usa para su resolución. A continuación evaluaremos el buen hacer del modelo numérico comparando...

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