相关论文: Strong solutions of semilinear matched microstruct…
Vertical equilibrium models have proven to be well suited for simulating fluid flow in subsurface porous media such as saline aquifers with caprocks. However, in most cases the dimensionally reduced model lacks the accuracy to capture the…
We investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media. Taking advantage of the inherent structure of the system that allows to deduce a scalar Generalized Porous Medium Equation for…
In recent work, two of the authors proposed a broad global well-posedness conjecture for cubic quasilinear dispersive equations in two space dimensions, which asserts that global well-posedness and scattering holds for small initial data in…
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…
Modeling coupled processes in fractured porous media -- flow, deformation, fracture mechanics, and thermal/chemical effects -- often relies on mixed dimensional multiphysics formulations. These systems are nonlinear and depend on physical…
In this work, we present an upscaled model for mixed dimensional coupled flow problem in fractured porous media. We consider both embedded and discrete fracture models (EFM and DFM) as fine scale models which contain coupled system of…
We show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier-Stokes/Cahn-Hilliard system with a solenoidal…
A novel regularized fracture model for crack propagation in porous media is proposed. Our model is obtained through homogenization theory and formal asymptotic expansions. We start with a regularized quasi-static fracture model posed in a…
We are interested in studying a system coupling the compressible Navier-Stokes equations with an elastic structure located at the boundary of the fluid domain. Initially the fluid domain is rectangular and the beam is located on the upper…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…
The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…
Linear stability of horizontal and inclined stratified channel flows of Newtonian/non-Newtonian shear-thinning fluids is investigated with respect to all wavelength perturbations. The Carreau model has been chosen for the modeling of the…
We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. For initial data in $H^s, s>\frac{d}{2}+1$, the…
We analyze the steady fluid flow in a porous medium containing a network of thin fissures i.e. width $\mathcal{O}(\epsilon)$, where all the cracks are generated by the rigid translation of a continuous piecewise $C^{1}$ functions in a fixed…
We consider a linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for…
This article establishes local strong well-posedness and global strong well-posedness close to constant equilibria of a model coupling the primitive equations of ocean and atmospheric dynamics with Hibler's viscous-plastic sea ice model. In…
This paper presents several test cases intended to be benchmarks for numerical schemes for single-phase fluid flow in fractured porous media. A number of solution strategies are compared, including a vertex and a cell-centered finite volume…
In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws…
We consider a nonlinear parabolic model that forces solutions to stay on a $L^2$-sphere through a nonlocal term in the equation. We study the local and global well-posedness on a bounded domain and the whole Euclidean space in the energy…
In this paper a special piecewise linear system is studied. It is shown that, under a mild assumption, the semi-smooth Newton method applied to this system is well defined and the method generates a sequence that converges linearly to a…