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We are interested in nonlinear hyperbolic systems in nonconservative form arising in fluid dynamics , and, for solutions containing shock waves, we investigate the convergence of finite difference schemes applied to such systems. According to Dal Maso, LeFloch, and Murat's theory, a shock wave theory for a given nonconservative system requires prescribing a… (More)

This paper is concerned with the development of well-balanced high order Roe methods for two-dimensional nonconservative hyperbolic systems. In particular, we are interested in extending the methods introduced in [4] to the two-dimensional case. We also investigate the well-balance properties and the consistency of the resulting schemes. We focus in… (More)

Shallow water equations are widely used in ocean and hydraulic engineering to model flows in rivers, reservoirs or coastal areas, among others applications. In the form considered in this paper, they constitute a hyperbolic system of conservation laws with a source term due to the bottom topography. In recent years, there has been increasing interest… (More)

The numerical solution of shallow water systems is useful for several applications related to geophysical flows but the big dimensions of the domains suggests the use of powerful accelerators to obtain numerical results in reasonable times. This paper addresses how to speed up the numerical solution of a first order well-balanced finite volume scheme for 2D… (More)

The goal of this article is to design robust and simple first order explicit solvers for one-dimensional nonconservative hyperbolic systems. These solvers are intended to be used as the basis for higher order methods for one or multidimensional problems. The starting point for the development of these solvers is the general definition of a Roe linearization… (More)

In this work we introduce a general family of finite volume methods for non-homogeneous hyperbolic systems with non-conservative terms. We prove that all of them are " asymptoti-cally well-balanced " : They preserve all smooth stationary solutions in all the domain but a set whose measure tends to zero as ∆x tends to zero. This theory is applied to solve… (More)

In this paper we present a new two-layer model of Savage-Hutter type to study submarine avalanches. A layer composed of fluidized granular material is assumed to flow within an upper layer composed of an inviscid fluid (e. g. water). The model is derived in a system of local coordinates following a non-erodible bottom and takes into account its curvature.… (More)

The two-layer shallow water system is used as the numerical model to simulate several phenomena related to geophysical flows such as the steady exchange of two different water flows, as occurs in the Strait of Gibraltar, or the tsunamis generated by underwater landslides. The numerical solution of this model for realistic domains imposes great demands of… (More)