CASTRO DÍAZ , Manuel Jesús

In this work, we present a class of fast first order finite volume solvers, named as PVM (Polynomial Viscosity Matrix), for balance laws or, more generally, for nonconservative hyperbolic systems. They are defined in terms of viscosity matrices computed by a suitable polynomial evaluation of a Roe matrix. These methods have the advantage that...

In this work, we present a general framework for vertical discretizations of Euler equations. It generalizes the usual moment and multilayer models and allows to obtain a family of multilayer-moment models. It considers a multilayer-type discretization where the layerwise velocity is a polynomial of arbitrary degree N on the vertical variable....

En este trabajo se presenta la extensión de los esquemas MUSTA (Multi-Stage) de alto orden a problemas no conservativos. En [7] E.F. Toro, V.A. Titarev, MUSTA Schemes for Systems of Conservation Laws. J. Comput. Phys., 216(2): 403 - 429, 2006 se presentaron los esquema de tipo MUSTA para leyes de conservación, usando como resolvedor de Riemann...

This paper focus on the numerical approximation of two-layer shallow water system. First, a new approximation of the eigenvalues of the system is proposed, which satisfies some interesting properties. From this approximation, we give an accurate estimation of the non-hyperbolic region, which improves significantly the one computed with the...

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...

Los modelos NPZ (siglas para Nutrientes-Fitoplancton-Zooplancton en ingl es) son com unmente utilizados en estudios de biolog a marina. Este tipo de modelos utiliza un conjunto de ecuaciones diferenciales muy sencillo para de nir la din amica del plancton marino. Las variables de estado de las cuales se modeliza su evoluci on son...

Presentamos un esquema de volúmenes finitos para la resolución de las ecuaciones de aguas someras con término fuente debido a la topografía del fondo. Se trata de un esquema de alto orden, bien equilibrado y capaz de afrontar situaciones en las que aparecen zonas secas. El esquema se ha desarrollado en un marco no conservativo general, y se...

Los modelos NPZ (siglas para Nutrientes-Fitoplancton-Zooplancton en inglés) son comúnmente utilizados en estudios de biología marina. Este tipo de modelos utiliza un conjunto de ecuaciones diferenciales muy sencillo para medir la dinámica del plancton marino. Las variables de estado de las cuales se modeliza su evolución son los nutrientes, el...

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 L2 linearly stable in that case. Then, we introduce a simple...

This paper is concerned with the numerical approximation of bedload sediment transport due to water evolution. For the hydrodynamical component we consider Shallow Water equations. The morphodynamical component is defined by a continuity equation, which is defined in function of the solid transport discharge. We present several deterministic...

En este trabajo se aborda la aproximación numérica del problema de arrastre de sedimentos causada por la evolución del agua. Para la componente hidrodinámica se consideran las ecuaciones de aguas poco profundas. La componente morfodinámica se define mediante una ecuación de continuidad, dada en función del caudal sólido. Ambas componentes...

We propose a multi-layer approach to simulate hyperpycnal and hypopycnal plumes in flows with free surface. The model allows to compute the vertical profile of the horizontal and the vertical components of the velocity of the fluid flow. The model can describe as well the vertical profile of the sediment concentration and the velocity...

In this paper, we propose a two-layer depth-integrated non-hydrostatic system with improved dispersion relations. This improvement is obtained through three free parameters: two of them related to the representation of the pressure at the interface and a third one that controls the relative position of the interface concerning the total height....

En este trabajo se estudia un nuevo modelo de tipo Savage-Hutter para avalanchas submarinas. El modelo obtenido es de tipo aguas someras bicapa en el que la capa superior representa al fluido y la capa inferior representa a un estrato de material granular. En la deducción del modelo se han tenido en cuenta diferentes leyes constitutivas en los...

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...

In this paper, we introduce a class of well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. We extend the derivation of standard finite volume solvers for homogeneous systems to non-homogeneous ones using the method of lines. We study conservation and some well-balanced properties of the numerical scheme. We apply our...