Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation.
New unilateral problems in stratigraphy
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 , 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...
Nguetseng's two-scale convergence method for filtration and seismic acoustic problems in elastic porous media.
Nonlinear diffusion from a delocalized source : affine self-similarity, time reversal, & nonradial focusing geometries
Nonlinear diffusion processes.
Nonlinear peristaltic transport of MHD flow through a porous medium.
Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations.
Non-negative solutions of generalized porous medium equations.
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.
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
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
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 methods for a model for wave propagation in composite anisotropic media
Numerical methods with interface estimates for the porous medium equation
Numerical modeling of heat exchange and unsaturated-saturated flow in porous media
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.
Numerical modeling of the simultaneous heat and moisture transfer
Numerical simulation of pollutant transport in fractured vuggy porous karstic aquifers.
Numerical Solution of Steady-State Porous Flow Free Boundary Problems.
Numerical solution of the Kiessl model
The Kiessl model of moisture and heat transfer in generally nonhomogeneous porous materials is analyzed. A weak formulation of the problem of propagation of the state parameters of this model, which are so-called moisture potential and temperature, is derived. An application of the method of discretization in time leads to a system of boundary-value problems for coupled pairs of nonlinear second order ODE’s. Some existence and regularity results for these problems are proved and an efficient numerical...
Numerical studies of groundwater flow problems with a singularity
The paper studies mesh dependent numerical solution of groundwater problems with singularities, caused by boreholes represented as points, instead of a real radius. We show on examples, that the numerical solution of the borehole pumping problem with point source (singularity) can be related to the exact solution of a regular problem with adapted geometry of a finite borehole radius. The radius providing the fit is roughly proportional to the mesh step. Next we define a problem of fracture-rock...