Γ-convergence and homogenization of functionals in Sobolev spaces with variable exponents

AbstractThis paper is devoted to homogenization and minimization problems for variational functionals in the framework of Sobolev spaces with continuous variable exponents. We assume that the sequence of exponents converges in the uniform metric and that the Lagrangian has a periodic microstructure. Then under natural coerciveness assumptions we prove a Γ-convergence result and, as a consequence, the convergence of minimizers (solutions to the corresponding Euler equations)

Estudi i modelització CFD d'un ejector

El present projecte es basa en l’estudi i la modelització CFD (Computacional Fluid Dynamics) d’un ejector amb aplicacions per l’aprofitament de l’hidrogen residual en el procés d’obtenció d’energia elèctrica en piles PEM. S’utilitzarà el software Comsol Multiphysics per fer les simulacions computacionals que permetran fer un estudi complet i precís del comportament del flux dins l’ejector. L’objectiu principal és obtenir les relacions entre les diferents geometries que ens permetran dimensionar l’ejector per tal de millorar el seu rendiment. Primer s’analitzen les pressions inicials òptimes de funcionament de l’ejector i s’estudien les geometries que tenen una influència directe en el seu rendiment. Es fa un estudi per trobar les possibles relacions entre les geometries més influents en el rendiment, que ens permetran dimensionar l’ejector de la manera més optimitzada possible. Finalment, es fan els canvis en la geometria del model estudiat inicialment, a partir de les relacions òptimes trobades, per tal d’observar si hi ha canvis destacables en els cabals i el rendiment. Els resultats ens mostren que el model final amb els canvis implementats, presenta una millora considerable en el rendiment per totes les condicions inicials de pressió estudiades. El model final és capaç d’induir més cabal màssic d’hidrogen que el model inicial, només fent una sèrie de canvis en les geometries.El presente proyecto se basa en el estudio y la modelización CFD (Computacional Fluid Dynamics) de un eyector con aplicaciones en el aprovechamiento del hidrogeno residual en el proceso de obtención de energía eléctrica en pilas PEM. Se utilizará el software Comsol Multiphysics para realizar las simulaciones computacionales que permitirán hacer un estudio completo y preciso del comportamiento del flujo dentro del eyector. El objetivo principal es obtener las relaciones entre las diferentes geometrías que nos permitirán dimensionar el eyector para mejorar su rendimiento. Primero se analizan las presiones iniciales óptimas de funcionamiento del eyector y se estudian las geometrías que tienen una influencia directa en su rendimiento. Se realiza un estudio para encontrar las posibles relaciones entre las geometrías más influyentes en el rendimiento, que nos permitirán dimensionar el eyector de la manera más optimizada posible. Finalmente, se realizan los cambios en la geometría del modelo estudiado inicialmente, a partir de las relaciones óptimas encontradas, a fin de observar si hay cambios destacables en los caudales y el rendimiento. Los resultados nos muestran que el modelo final con los cambios implementados presenta una mejora considerable en el rendimiento para todas las condiciones iniciales de presión estudiadas. El modelo final es capaz de inducir un mayor caudal másico de hidrógeno que el modelo inicial, sólo haciendo una serie de cambios en las geometrías.This project is based on the study and CFD (Computational Fluid Dynamics) modeling of an ejector with applications in the use of residual hydrogen in the process of obtaining electrical energy in PEM batteries. The Comsol Multiphysics software will be used to perform the computational simulations that will allow a complete and accurate study of the flow behavior inside the ejector. The main objective is to obtain the relationships between the different geometries that will allow us to size the ejector to improve its performance. First, the optimal initial operating pressures of the ejector are analyzed and the geometries that have a direct influence on its performance are studied. A study is carried out to find the possible relationships between the most influential geometries on performance, which will allow us to size the ejector in the most optimized way possible. Finally, changes are made in the geometry of the model initially studied, based on the optimal relationships found, to observe if there are any notable changes in flows and performance. The results show us that the final model with the implemented changes presents a considerable improvement in performance for all the initial pressure conditions studied. The final model can induce a higher mass flow rate of hydrogen than the initial model, just by making some changes in the geometries

Approximating the vanishing capillarity limit of two-phase flow in multi-dimensional heterogeneous porous medium

International audienceNeglecting capillary pressure effects in two-phase flow models for porous media may lead to non-physical solutions: indeed, the physical solution is obtained as limit of the parabolic model with small but non-zero capillarity. In this paper, we propose and compare several numerical strategies designed specifically for approximating physically relevant solutions of the hyperbolic model with neglected capillarity, in the multi-dimensional case. It has been shown in [Andreianov&Canc'es, Comput. Geosci., 2013, to appear] that in the case of the one-dimensional Buckley-Leverett equation with distinct capillary pressure properties of adjacent rocks, the interface may impose an upper bound on the transmitted flux. This transmission condition may reflect the oil trapping phenomenon. We recall the theoretical results for the one-dimensional case which are used to motivate the construction of multi- dimensional finite volume schemes. We describe and compare a coupled scheme resulting as the limit of the scheme constructed in [Brenner & Canc'es & Hilhorst, HAL preprint no.00675681, 2012) and two IMplicit Pressure - Explicit Saturation (IMPES) schemes with different level of coupling

Numerical prediction of saturation in dual scale fibrous reinforcements during Liquid Composite Molding

This paper presents a fractional flow model based on two-phase flow, resin and air, through a porous medium to simulate numerically Liquid Composites Molding (LCM) processes. It allows predicting the formation, transport and compression of voids in the modeling of LCM. The equations are derived by combining Darcy’s law and mass conservation for each phase (resin/air). In the model, the relative permeability and capillary pressure depend on saturation. The resin is incompressible and the air slightly compressible. Introducing some simplifications, the fractional flow model consists of a saturation equation coupled with a pressure/velocity equation including the effects of air solubility and compressibility. The introduction of air compressibility in the pressure equation allows for the numerical prediction of the experimental behavior at low constant resin injection flow rate. A good agreement was obtained between the numerical prediction of saturation in a glass fiber reinforcement and the experimental observations during the filling of a test mold by Resin Transfer Molding (RTM). 2015 Elsevier Ltd. All rights reserved.The authors acknowledge financial support of the Spanish Government (Project DPI2013-44903-R-AR).Gascón Martínez, ML.; García Manrique, JA.; Lebel, F.; Ruiz, E.; Trochu, F. (2015). Numerical prediction of saturation in dual scale fibrous reinforcements during Liquid Composite Molding. Composites Part A: Applied Science and Manufacturing. 77:275-284. https://doi.org/10.1016/j.compositesa.2015.05.019S2752847