Catálogo de publicaciones - libros

In this paper a new family of Hölder continuous functions are presented. Using the properties of this family it is possible to generalized the classical Harten’s subcell resolution theory and to apply it for the discretization of piecewise Hölder continuous functions. Some numerical experiments that confirm the theoretical results are presented.

We study mathematical models for static grain deep-bed drying. These models take the general form of hyperbolic semilinear systems. The solutions vary strongly at the beginning of the drying process, so that the use of second order semiimplicit schemes is useful. Numerical experiments show a good qualitative behaviour of our approximations.

We study the numerical approximation of a system from the physics of compressible turbulent flows, in the regime of large Reynolds numbers. The PDE model takes the form of a nonconservative hyperbolic system with singular viscous perturbations. Weak solutions of the limit system are regularization dependent and classical approximate Riemann solvers are known to grossly fail in the capture of shock solutions. Here, the notion of kinetic functions is used to derive a complete set of generalized jump conditions which keeps a precise memory of the underlying viscous mechanism. To enforce for validity these jump conditions, we propose a hybrid Godunov-Glimm method coupled with a local nonlinear correction procedure.

Harten’s interpolatory multiresolution representation of data [2] has been extended in the case of point-value discretization to include Hermite interpolation by Warming and Beam in [3]. In this work we extend Harten’s framework for multiresolution analysis to the vector case for cell-averaged data, focusing on Hermite interpolatory techniques. Some numerical experiments compare the algorithm with some well known scalar methods.

This work is concerned with the numerical approximation of Cauchy problems for one-dimensional nonconservative hyperbolic systems, for which it is assumed that each characteristic field is either genuinely nonlinear or linearly degenerate. The theory developed by Dal Maso, LeFloch and Murat [1] is used to define the concept of weak solutions of these systems, giving a sense to nonconservative products as Borel measures, based on the choice of a family of paths in the phases space. We establish some basic hypotheses concerning this family of paths which ensure the fulfilling of some good properties for weak solutions. A family of paths satisfying these hypotheses can be constructed at least for states that are close enough. In particular, we prove that the choice of such a family allows to write the Godunov method for a nonconservative system in a simple and general manner. The previous results are applied to a linear balance law, for which the Godunov method can be explicitly written and easily implemented.

A new FCT-based algorithm is presented for conservative, local bounds preserving interpolations, necessary in the remapping step of Arbitrary Lagrangian- Eulerian (ALE) simulations. To avoid overrestriction of high-order fluxes, caused by separate processing of variables, the method incorporates particular conservation laws incrementally. Contrary to popular a posteriori correction methods, it utilizes physical information about the modeled process already during the remapping step. Moreover, extension to multiple dimensions is trivial.

In this paper we propose and test a new non-affine concept of hierarchic higher-order finite elements (-FEM) suitable for symmetric linear elliptic problems. The energetic inner product induced by the elliptic operator is used to construct partially orthonormal shape functions which automatically eliminate all internal degrees of freedom from the stiffness matrix. The stiffness matrix becomes smaller and better-conditioned compared to standard types of higher-order shape functions. The orthonormalization algorithm is elementwise local and therefore easily parallelizable. The procedure is extendable to nonsymmetric elliptic problems. Numerical examples including performance comparisons to other popular sets of higher-order shape functions are presented.

It is well known that the design of suitable higher-order shape functions is essential for the performance of the -FEM. In this paper we propose a new family of hierarchic higher-order edge elements for the time-harmonic Maxwell’s equations which are capable of reducing the condition number of the stiffness matrices dramatically compared to the currently best known hierarchic edge elements. The excellent conditioning properties of the new elements are illustrated by numerical examples.

A thermodynamically consistent finite-volume numerical algorithm for martensitic phase-transition front propagation is described in the paper. The proposed numerical method generalizes the wave-propagation algorithm to the case of moving discontinuities in thermoelastic solids.

In this work we consider the homogenization process in Aluminum alloys, in which inhomogeneities dissolve. This process is governed by diffusion, and mass conservation leads to the Stefan condition on the moving interface. The Level Set Method is used to model this problem, due to its convenience to handle merging/ breaking interfaces, compared with other available methods. In binary alloys, the interface concentration is the solid solubility predicted from thermodynamics. However, in multicomponent alloys, the interface concentrations must satisfy a hyperbolic coupling, and therefore, have to be found as part of the solution. In this work we present a computational method to solve three-dimensional dissolution of binary alloys, and we study its extension to multicomponent alloys. In this respect, we restrict ourselves to one-dimensional problems and we focus our attention in the solution of the nonlinear coupled system of diffusion equations.