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Modelling bioremediation of polluted soils in unsaturated condition and its effect on the soil hydraulic properties

Iacopo Borsi, Angiolo Farina, Antonio Fasano, Mario Primicerio (2008)

Applications of Mathematics

We study the unsaturated flow of an incompressible liquid carrying a bacterial population through a porous medium contaminated with some pollutant. The biomass grows feeding on the pollutant and affecting at the same time all the physics of the flow. We formulate a mathematical model in a one-dimensional setting and we prove an existence theorem for it. The so-called fluid media scaling approach, often used in the literature, is discussed and its limitations are pointed out on the basis of a specific...

Mortar finite element discretization of a model coupling Darcy and Stokes equations

Christine Bernardi, Tomás Chacón Rebollo, Frédéric Hecht, Zoubida Mghazli (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations are coupled via appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the flow inside and outside the porous medium. We prove a priori and a posteriori error estimates for the resulting discrete problem. Some numerical experiments...

New unilateral problems in stratigraphy

Stanislav N. Antontsev, Gérard Gagneux, Robert Luce, Guy Vallet (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type 0 ∈ ∂ t u - d i v { H ( ∂ t u + E ) ∇ u } , where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation...

Non-negative solutions of generalized porous medium equations.

Bjorn E. J. Dahlberg, Carlos E. Kenig (1986)

Revista Matemática Iberoamericana

The purpose of this paper is to study nonnegative solutions u of the nonlinear evolution equations∂u/∂t = Δφ(u),  x ∈ Rn, 0 < t < T ≤ +∞  (1.1)Here the nonlinearity φ is assumed to be continuous, increasing with φ(0) = 0. This equation arises in various physical problems, and specializing φ leads to models for nonlinear filtrations, or for the gas flow in a porous medium. For a recent survey in these equations see [9].The main object of this work is to study the initial value problem...

Non-negative solutions to fast diffusions.

Bjorn E. J. Dahlberg, Carlos E. Kenig (1988)

Revista Matemática Iberoamericana

The purpose of this work is to study the class of non-negative continuous weak solutions of the non-linear evolution equation∂u/∂t = ∆φ(u),   x ∈ Rn, 0 < t < T ≤ +∞.

Numerical homogenization of well singularities in the flow transport through heterogeneous porous media: fully discrete scheme

Meiqun Jiang, Xingye Yue (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Motivated by well-driven flow transport in porous media, Chen and Yue proposed a numerical homogenization method for Green function [Multiscale Model. Simul.1 (2003) 260–303]. In that paper, the authors focused on the well pore pressure, so the local error analysis in maximum norm was presented. As a continuation, we will consider a fully discrete scheme and its multiscale error analysis on the velocity field.

Numerical investigation of dynamic capillary pressure in two-phase flow in porous medium

Radek Fučík, Jiří Mikyška (2011)

Mathematica Bohemica

In order to investigate effects of the dynamic capillary pressure-saturation relationship used in the modelling of a flow in porous media, a one-dimensional fully implicit numerical scheme is proposed. The numerical scheme is used to simulate an experimental procedure using a measured dataset for the sand and fluid properties. Results of simulations using different models for the dynamic effect term in capillary pressure-saturation relationship are presented and discussed.

Numerical modeling of heat exchange and unsaturated-saturated flow in porous media

Kačur, Jozef, Mihala, Patrik, Tóth, Michal (2017)

Proceedings of Equadiff 14

We discuss the numerical modeling of heat exchange between the infiltrated water and porous media matrix. An unsaturated-saturated flow is considered with boundary conditions reflecting the external driven forces. The developed numerical method is efficient and can be used for solving the inverse problems concerning determination of transmission coefficients for heat energy exchange inside and also on the boundary of porous media. Numerical experiments support our method.

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