Rafael Muñoz-Sola

THE WATER CONVEYANCE PROBLEM: OPTIMAL PURIFICATION OF POLLUTED WATERS

In this work we deal with the optimal purification of polluted areas of shallow waters by means of the injection of clear water in order to promote seawater exchange. This problem can be formulated as a control constrained optimal control problem where the control is the velocity of the injected water, the state equations are the shallow water equations together with that modelling the contaminant concentration, and the cost function measures the total amount of injected water and the fulfilment of the water quality standards. We analyze the solutions of the optimal control problem and give an optimality condition in order to characterize them. We also discretize the problem by means of a characteristics-mixed finite element method, focusing our attention on both the discrete and the discretized adjoint systems, and propose an algorithm for the numerical resolution of the discrete optimization problem. Finally, we present numerical results for some computational experiments.

THEORETICAL AND NUMERICAL STUDY OF AN IMPLICIT DISCRETIZATION OF A 1D INVISCID MODEL FOR RIVER FLOWS

In this paper, we consider a 1D inviscid model to simulate river flows whose unknown are the water elevation, the flow rate and the wet area. We rewrite this model in terms of the wet area and the flow rate. Next, by using a weak formulation and a discretization by characteristics, we derive an implicit semidiscretized scheme that involves a variational inequality. Under suitable hypothesis, we prove that this scheme has at least one solution. We present an algorithm for the numerical solution of the fully discretized problem and the numerical results obtained for channels with parabolic and rectangular sections and variable depth. Finally, we perform a stability analysis for the semidiscretized scheme applied to a similar problem where the convection term has been omitted.

About the solution of the even parity formulation of the transient radiative heat transfer equations

This paper studies the existence and uniqueness questions, in classical spaces, for a certain system of differential equations. From the physical point of view, the interest of this system lies in that it becomes, for particular choices of its coefficients, the even parity formulation of the S2 approximation of the transient radiative heat transfer equations in the one-dimensional slab. A priori lower and upper bounds of the solution are obtained as well.ResumenEste artículo aborda las cuestiones de existencia y unicIDad, en espacios clásicos, para cierto sistema de ecuaciones diferenciales. Desde el punto de vista físico, el interés de este sistema radica en que se convierte, para elecciones particulares de sus coeficientes, en la formulación par de la aproximación S2 de las ecuaciones evolutivas de la tranferencia de calor por radiación en una geometría de laja (slab) unIDimensional. Asimismo, se obtienen cotas a priori, tanto inferiores como superiores, de la solución.

A transient eddy current problem on a moving domain. Numerical analysis

The aim of this paper is to introduce and analyze a numerical method to solve a transient eddy current problem which arises from the modeling of electromagnetic forming in the axisymmetric case. The resulting problem is degenerate parabolic with the time derivative acting on a moving subdomain. This paper is the sequel of Bermúdez et al. (SIAM J. Math. Anal. 45, 3629–3650, 2013), where a weak formulation of this problem was proved to be well posed and additional regularity of the solution was also established. In the present paper, we propose a finite element method in space combined with a backward Euler time scheme for its numerical solution. We obtain error estimates and report numerical results which allow us to assess the performance of the proposed method.

About the solution of the even parity formulation of the transient radiative heat transfer equations Sobre la solución de la formulación par de las ecuaciones evolutivas de transferencia de calor por radiación

Abstract This paper studies the existence and uniqueness questions, in classical spaces, for a certain system of differential equations. From the physical point o f view, the interest of this system lies in that it becomes, for particular choices of its coefficients, the e v n parity formulation of theS2 approximation of the transient radiative heat transfer equations in the on e-dimensional slab. A priori lower and upper bounds of the solution are obtained as well.

A Three-Dimensional Eutrophication Model: Analysis and Control

Eutrophication of lakes, reservoirs, streams, and coastal areas is one of the most widespread environmental problems of large water bodies. Eutrophication consists of unnatural enrichment with two plant nutrients: nitrogen and phosphorus. This overnutrification causes undesirable changes in water resources: excessive production of algae, deterioration of water quality and availability, fish kills, health hazards for humans, etc. Controlling the eutrophication is important in order to mitigate and remedy the problem.