Březina, Jan (2010)
Programs and Algorithms of Numerical Mathematics
Richards' equation is a widely used model of partially saturated flow in a porous medium. In order to obtain conservative velocity field several authors proposed to use mixed or mixed-hybrid schemes to solve the equation. In this paper, we shall analyze the mixed scheme on 1D domain and we show that it violates the discrete maximum principle which leads to catastrophic oscillations in the solution.
Monakhov, V.N. (2002)
Sibirskij Matematicheskij Zhurnal
José Carrillo, Gianni Gilardi (1990)
Annales de la Faculté des sciences de Toulouse : Mathématiques
Jean Dolbeault, Grzegorz Karch (2006)
Banach Center Publications
This note is devoted to the study of the long time behaviour of solutions to the heat and the porous medium equations in the presence of an external source term, using entropy methods and self-similar variables. Intermediate asymptotics and convergence results are shown using interpolation inequalities, Gagliardo-Nirenberg-Sobolev inequalities and Csiszár-Kullback type estimates.
Bunoiu, R., Saint Jean Paulin, Jeannine (1999)
Portugaliae Mathematica
B.H. Gilding, M.A. Herrero (1988)
Mathematische Annalen
Jean Dolbeault, Javier Fernández (2008)
Annales de l'I.H.P. Analyse non linéaire
Pal Dulal, Veerabhadraiah, R., Shivakumar, P.N., Rudraiah, N. (1984)
International Journal of Mathematics and Mathematical Sciences
Hayat, Tasawar, Wang, Yongqi (2003)
Mathematical Problems in Engineering
Peter Knabner, Jean E. Roberts (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy−Forchheimerlaw while that in the surrounding matrix is governed by Darcy’s law. We give an appropriate mixed, variational formulation and show existence and uniqueness of the solution. To show existence we give an analogous formulation for the model in which the Darcy−Forchheimerlaw is the governing equation throughout the domain. We show existence and uniqueness of the solution...
Beneš, Michal, Krupička, Lukáš (2019)
Programs and Algorithms of Numerical Mathematics
In this contribution we propose a model of coupled heat and moisture transport in variable saturated deformed porous media. Solution of this model provides temperature, moisture content and strain as a function of space and time. We present the detailed description of the model and a~numerical illustrative example.
Kamyar Malakpoor, Enrique F. Kaasschieter, Jacques M. Huyghe (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory in which a deformable and charged porous medium is saturated with a fluid with dissolved ions. Four components are defined: solid, liquid, cations and anions. The aim of this paper is the construction of the Lagrangian model of the four-component system. It is shown that, with the choice of Lagrangian description of the solid skeleton, the motion of the other components can be described in terms of...
Robert Eymard, Raphaèle Herbin, Anthony Michel (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Models of two phase flows in porous media, used in petroleum engineering, lead to a system of two coupled equations with elliptic and parabolic degenerate terms, and two unknowns, the saturation and the pressure. For the purpose of their approximation, a coupled scheme, consisting in a finite volume method together with a phase-by-phase upstream weighting scheme, is used in the industrial setting. This paper presents a mathematical analysis of this coupled scheme, first showing that it satisfies...
Robert Eymard, Raphaèle Herbin, Anthony Michel (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Models of two phase flows in porous media, used in petroleum engineering, lead to a system of two coupled equations with elliptic and parabolic degenerate terms, and two unknowns, the saturation and the pressure. For the purpose of their approximation, a coupled scheme, consisting in a finite volume method together with a phase-by-phase upstream weighting scheme, is used in the industrial setting. This paper presents a mathematical analysis of this coupled scheme, first showing that it satisfies...
Frolkovič, P. (1998)
Acta Mathematica Universitatis Comenianae. New Series
Mohamed Amara, Daniela Capatina-Papaghiuc, Bertrand Denel, Peppino Terpolilli (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature....
Mohamed Amara, Daniela Capatina-Papaghiuc, Bertrand Denel, Peppino Terpolilli (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature....
V. V. Kozlov (2009)
Mathematical Modelling of Natural Phenomena
The paper is devoted to mathematical modelling and numerical computations of a nonstationary free boundary problem. The model is based on processes of molecular diffusion of some products of chemical decomposition of a solid organic substance concentrated in bottom sediments. It takes into account non-stationary multi-component and multi-stage chemical decomposition of organic substances and the processes of sorption desorption under aerobic and anaerobic conditions. Such a model allows one to...
G. Gagneux, A.-M. Lefevere, M. Madaune-Tort (1988)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Z. Nowak, A. Stachurski (2003)
Control and Cybernetics