Related papers: A linear domain decomposition method for two-phase…
We propose an efficient iterative method to solve the mixed Stokes-Dracy model for coupling fluid and porous media flow. The weak formulation of this problem leads to a coupled, indefinite, ill-conditioned and symmetric linear system of…
The problem of the flow trough a porous media is formulated in terms of a pressure equation, based on arguments of volume conservation which state the mechanical equilibrium between the solid and the fluid phases. In the resulting governing…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
In this paper, we investigate the speed of convergence and higher-order asymptotics of solutions to the porous medium equation posed in $\mathbf{R}^N$. Applying a nonlinear change of variables, we rewrite the equation as a diffusion on a…
In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed…
In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely…
We consider a two-phase Darcy flow in a fractured and deformable porous medium for which the fractures are described as a network of planar surfaces leading to so-called hybrid-dimensional models. The fractures are assumed open and filled…
This paper deals with the efficient numerical solution of single-phase flow problems in fractured porous media. A monolithic multigrid method is proposed for solving two-dimensional arbitrary fracture networks with vertical and/or…
A numerical method for processing the data of ground penetrating radars for a piece-wise continuous layered medium is proposed. The method combines the layer stripping technique with numerical continuation of data into the complex…
In this study, we investigate the appeared complexity of two-phase flow (air-water) in a heterogeneous soil where the supposed porous media is non-deformable media which is under the time-dependent gas pressure. After obtaining of governing…
We extend the two-scale expansion approach of periodic homogenization to include time scales and thus can tackle the full instationary Navier-Stokes-Cahn-Hilliard model at the pore scale as microscale. Time scale separation allows us to…
In this paper, we consider a non-local (in time) two-phase flow model. The non-locality is introduced through the wettability alteration induced dynamic capillary pressure function. We present a monotone fixed-point iterative linearization…
Simulating the flow of two fluid phases in porous media is a challenging task, especially when fractures are included in the simulation. Fractures may have highly heterogeneous properties compared to the surrounding rock matrix,…
The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…
In this work, we study the parallel-in-time iterative solution of coupled flow and geomechanics in porous media, modelled by a two-field formulation of the Biot's equations. In particular, we propose a new version of the fixed stress…
The Richards equation, a nonlinear elliptic parabolic equation, is widely used to model infiltration in porous media. We develop a finite element method for solving the Richards equation by introducing a new bounded auxiliary variable to…
In this work, we propose a new model for flow through deformable porous media, where the solid material has two phases with distinct material properties. The two phases of the porous material follow a Cahn-Hilliard type evolution, with…
We model multi-dimensional two-phase flows of incompressible fluids in porous media using generalized Forchheimer equations and the capillary pressure. Firstly, we find a family of steady state solutions whose saturation and pressure are…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
In this paper we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media proposed in [19]. The starting point is the pore scale model in [12], which is a…