Manuel Jesús Castro Díaz

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This paper is concerned with the development of high order methods for the numerical approximation of one-dimensional nonconservative hy-perbolic systems. In particular, we are interested in high order extensions of the generalized Roe methods introduced by I. Toumi in 1992, based on WENO reconstruction of states. We also investigate the well-balanced(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)
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 goal of this article is to design a new approximate Riemann solver for the two-layer shallow water system which is fast compared to Roe schemes and accurate compared to Lax-Friedrichs, FORCE, or GFORCE schemes (see [14]). This Riemann solver is based on a suitable decomposition of a Roe matrix (see [27]) by means of a parabolic viscosity matrix (see(More)
In this work, a characterization of the hyperbolicity region for the two layer shallow-water system is proposed and checked. Next, some path-conservative finite volume schemes (see [11]) that can be used even if the system is not hyperbolic are presented, but they are not in general L 2 linearly stable in that case. Then, we introduce a simple but efficient(More)
Keywords: Nonconservative hyperbolic system Shock wave Family of paths Equivalent equation Convergence error measure Formally path-consistent scheme a b s t r a c t 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(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)