Related papers: A Fully Equivalent Global Pressure Formulation for…
In this paper, we consider the three dimensional Cauchy problem of the compressible micropolar viscous flows, we prove the existence of unique global classical solution for smooth initial data with small initial energy but possibly large…
The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of…
An outstanding characteristic of porous media, desired in many applications, is the large surface area, which facilitates solid-fluid interactions, making porous media an extreme case in colloid and interface science. In two-fluid systems,…
In this paper we show the global well-posedness of solutions to a three-dimensional magnetohydrodynamical (MHD) model in porous media. Compared to the classical MHD equations, our system involves a nonlinear damping term in the momentum…
The majority of available numerical algorithms for interfacial two-phase flows either treat both fluid phases as incompressible (constant density) or treat both phases as compressible (variable density). This presents a limitation for the…
We consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analysis for this model. We study a splitting formulation where a…
We report the results of a study of multiphase flow in porous media. A Darcy's law for steady multiphase flow was investigated for both binary and ternary amphiphilic flow. Linear flux-forcing relationships satisfying Onsager reciprocity…
We present a reduction-consistent and thermodynamically consistent formulation and an associated numerical algorithm for simulating the dynamics of an isothermal mixture consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids…
This paper is concerned with the three-dimensional equations of a simplified hydrodynamic flow modeling the motion of compressible, nematic liquid crystal materials. The authors establish the global existence of classical solution to the…
Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains $\Omega_{t +}, \Omega_{t -} \subset \mathbb{R}^N$, $N \ge 2$, where the domains are separated by a…
The transport of single-phase fluid mixtures in porous media is described by cross-diffusion equations for the mass densities. The equations are obtained in a thermodynamic consistent way from mass balance, Darcy's law, and the van der…
A two-phase model and its application to wavefields numerical simulation are discussed in the context of modeling of compressible fluid flows in elastic porous media. The derivation of the model is based on a theory of thermodynamically…
We consider the evolution of two-dimensional incompressible flows with variable density, only bounded and bounded away from zero. Assuming that the initial velocity belongs to a suitable critical subspace of L^2 , we prove a global-in-time…
Understanding the flow of yield stress fluids in porous media is a major challenge. In particular, experiments and extensive numerical simulations report a non-linear Darcy law as a function of the pressure gradient. In this letter, we…
This work presents a unified numerical framework for simulating incompressible flows within the coupled fluid-porous-medium system and involving heat and solute transport and phase-changing process. A complete set of governing equations is…
The modeling of flow and heat transfer in porous media systems have always been a challenge and, the extended Darcy transport models for flow and equilibrium and non-equilibrium energy models for heat transfer are being used for macro-level…
The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pressure gradient, according to Darcy's law, and the pressure is…
A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. It is argued that this new pressure equation allows unifying…
In this paper, we construct a class global large solution to the 3D incompressible micropolar fluid system. Precisely speaking, by choosing a special initial data which can be arbitrarily large in $\dot{B}^{-1}_{\infty,\infty}$, the system…
In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy's law. We show formation of singularities with infinite energy and for finite energy we obtain…