Catálogo de publicaciones - libros

We present a multilayer Saint-Venant system for the simulation of 3D free surface flows. A precise analysis of the shallow water assumption leads to a set of coupled Saint-Venant type systems. For each time dependent layer, a Saint-Venant type system is solved on the same 2D mesh by a kinetic solver using a finite volume framework. We validate the model by comparisons with Navier-Stokes solutions.

This paper is concerned with the numerical approximation of bed-load sediment transport due to water evolution. We introduce an unified formulation for several bed-load models. Some numerical simulations are presented.

We review a conservative finite difference shock capturing scheme that has been used by our research team over the last years for the numerical simulations of complex flows [3, 6]. This scheme is based on Shu and Osher’s technique [9] for the design of highly accurate finite difference schemes obtained by flux reconstruction procedures (ENO, WENO) on Cartesian meshes and Donat-Marquina’s flux splitting [4]. We then motivate the need for mesh adaptivity to tackle realistic hydrodynamic simulations on two and three dimensions and describe some details of our (AMR) ([2, 7]) implementation of the former finite difference scheme [1]. We finish the work with some numerical experiments that show the benefits of our scheme.

The accuracy of low order numerical methods for the shallow water equations is improved by using vector reconstruction techniques based on matrix valued radial basis functions. Applications to geophysical fluid dynamics problems show that these reconstruction techniques allow to maintain important discrete conservation properties while greatly reducing the error with respect to low order discretizations.

We investigate the hierarchical structure of hexagonal kinetic models as a tool for the numerical simulation of the Boltzmann equation. This is of use for a number of applications, e.g. in the context of domain decomposition and of multigrid techniques.

The paper deals with a construction of an adaptive mesh in the framework of the cell-centred finite volume scheme. The adaptive strategy is applied to the numerical solution of problems governed by hyperbolic partial differential equations. Starting from the adaptation techniques for the stationary problems (for a general overview see e.g. [9]), the nonstationary case is studied. The main attention is paid to an adaptive part of a time marching procedure. The of the proposed method is to keep the mass conservation of the numerical solution at each adaptation step. We apply an anisotropic mesh adaptation from [1]. This is followed by a recovery of the approximate solution on the new mesh satisfying the geometric conservation law. The adaptation algorithm is formulated in the framework of an N-dimensional numerical solution procedure. A new strategy for moving a vertex of the mesh, based on a gradient method, is presented. The results from [4] are further developed. The of the proposed method is the ability to solve problems with moving discontinuities. A numerical example is presented.

A slope limiting approach to the design of recovery based error indicators for finite element discretizations is presented. The smoothed gradient field is recovered at edge midpoints by means of limited averaging of adjacent slope values. As an alternative, the constant gradient values may act as upper and lower bounds to be imposed on edge gradients resulting from traditional reconstruction techniques such as averaging projection or discrete patch recovery schemes. In either case, the difference between consistent and reconstructed gradient values measured in the -norm provides a usable indicator for grid adaptivity.

We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. Numerical experiments confirm the superconvergence property and suggest that it holds also for the lowest order Brezzi-Douglas- Marini approximation.

The research presented is focused on a comparative study of a posteriori error estimation methods to various approximations of the Stokes problem. Mainly, we are interested in the performance of functional type a posterior error estimates and their comparison with other methods.

The modeling of numerous industrial processes leads to multifield problems, which are governed by the coupled interaction of several physical fields. As an example, consider electromagnetic forming, where the evolution of the deformation field of a mechanical structure consisting of well conducting material is coupled with an electromagnetic field, triggering a Lorentz force, which drives the deformation process. The purpose of the work reported on here is to develop techniques for a posteriori error control for the finite element approximation to the solution of certain systems of two boundary value problems that are coupled via their coefficients and their right-hand sides. As a first step, an error estimator for the right-hand side of the mechanical subsystem is presented in the case of a simplified model problem for the electromagnetic system. The particular influence of the mixed character of the evolution equations is discussed for a numerical example.