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A novel approach to modelling of flow in fractured porous medium

Jan Šembera, Jiří Maryška, Jiřina Královcová, Otto Severýn (2007)

Kybernetika

There are many problems of groundwater flow in a disrupted rock massifs that should be modelled using numerical models. It can be done via “standard approaches” such as increase of the permeability of the porous medium to account the fracture system (or double-porosity models), or discrete stochastic fracture network models. Both of these approaches appear to have their constraints and limitations, which make them unsuitable for the large- scale long-time hydrogeological calculations. In the article,...

A parallel algorithm for two phase multicomponent contaminant transport

Todd Arbogast, Clint N. Dawson, Mary F. Wheeler (1995)

Applications of Mathematics

We discuss the formulation of a simulator in three spatial dimensions for a multicomponent, two phase (air, water) system of groundwater flow and transport with biodegradation kinetics and wells with multiple screens. The simulator has been developed for parallel, distributed memory, message passing machines. The numerical procedures employed are a fully implicit expanded mixed finite element method for flow and either a characteristics-mixed method or a Godunov method for transport and reactions...

A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems

Alexandre Ern, Sébastien Meunier (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We analyze Euler-Galerkin approximations (conforming finite elements in space and implicit Euler in time) to coupled PDE systems in which one dependent variable, say u , is governed by an elliptic equation and the other, say p , by a parabolic-like equation. The underlying application is the poroelasticity system within the quasi-static assumption. Different polynomial orders are used for the u - and p -components to obtain optimally convergent a priori bounds for all the terms in the error energy norm....

A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems

Alexandre Ern, Sébastien Meunier (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze Euler-Galerkin approximations (conforming finite elements in space and implicit Euler in time) to coupled PDE systems in which one dependent variable, say u, is governed by an elliptic equation and the other, say p, by a parabolic-like equation. The underlying application is the poroelasticity system within the quasi-static assumption. Different polynomial orders are used for the u- and p-components to obtain optimally convergent a priori bounds for all the terms in the error energy...

A reduced model for Darcy’s problem in networks of fractures

Luca Formaggia, Alessio Fumagalli, Anna Scotti, Paolo Ruffo (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Subsurface flows are influenced by the presence of faults and large fractures which act as preferential paths or barriers for the flow. In literature models were proposed to handle fractures in a porous medium as objects of codimension 1. In this work we consider the case of a network of intersecting fractures, with the aim of deriving physically consistent and effective interface conditions to impose at the intersection between fractures. This new model accounts for the angle between fractures...

A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems

Hideki Murakawa (2009)

Kybernetika

This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion...

A stationary flow of fresh and salt groundwater in a heterogeneous coastal aquifer

S. Challal, A. Lyaghfouri (2000)

Bollettino dell'Unione Matematica Italiana

Si stabilisce l'esistenza e l'unicità di una soluzione monotona per il problema di frontiera libera correlato al flusso stazionare d'acqua dolce e salata intorno ad un acquifero eterogeneo. Si provano la continuità e l'esistenza di un limite asintotico della frontiera libera.

A two-fluid hyperbolic model in a porous medium

Laëtitia Girault, Jean-Marc Hérard (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper is devoted to the computation of two-phase flows in a porous medium when applying the two-fluid approach. The basic formulation is presented first, together with the main properties of the model. A few basic analytic solutions are then provided, some of them corresponding to solutions of the one-dimensional Riemann problem. Three distinct Finite-Volume schemes are then introduced. The first two schemes, which rely on the Rusanov scheme, are shown to give wrong approximations in some...

A viscoelastic model with non-local damping application to the human lungs

Céline Grandmont, Bertrand Maury, Nicolas Meunier (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we elaborate a model to describe some aspects of the human lung considered as a continuous, deformable, medium. To that purpose, we study the asymptotic behavior of a spring-mass system with dissipation. The key feature of our approach is the nature of this dissipation phenomena, which is related here to the flow of a viscous fluid through a dyadic tree of pipes (the branches), each exit of which being connected to an air pocket (alvelola) delimited by two successive masses. The...

Air entrainment in transient flows in closed water pipes : A two-layer approach

C. Bourdarias, M. Ersoy, Stéphane Gerbi (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas). The obtained system is conditionally hyperbolic. Then, we propose a mathematical kinetic interpretation of this system to finally construct a two-layer kinetic scheme...

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