English
Related papers

Related papers: Global existence for a two-phase flow model with c…

200 papers

We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…

Analysis of PDEs · Mathematics 2022-06-14 Mohamed Majdoub , Nasser-eddine Tatar

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…

Analysis of PDEs · Mathematics 2024-04-04 Raphaël Danchin

Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…

Fluid Dynamics · Physics 2025-02-25 Emma M. Boyd , Eric Sandall , Maycon Meier , J. Matt Quinlan , Brandon Runnels

We study the expanded mixed finite element method applied to degenerate parabolic equations with the Dirichlet boundary condition. The equation is considered a prototype of the nonlinear Forchheimer equation, a inverted to the nonlinear…

Numerical Analysis · Mathematics 2014-10-01 Akif Ibragimov , Thinh T. Kieu

We study the equations of a two dimensional incompressible Newtonian fluid coupled with a dispersive parabolic-elliptic system on bounded domains. Global in time weak solutions are shown to exist and converge with a rate to the stationary…

Analysis of PDEs · Mathematics 2008-10-14 Rolf J. Ryham

The paper is devoted to the derivation, by linearization, of simplified (fully homogenized) homogenized models of an immiscible incompressible two-phase flow in double porosity media in the case of thin fissures. In a simplified dual…

Analysis of PDEs · Mathematics 2022-11-14 Mladen Jurak , Leonid Pankratov , Anja Vrbaški

We propose and analyze a combined finite volume--nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is…

Numerical Analysis · Mathematics 2013-06-13 Bilal Saad , Mazen Saad

We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…

Analysis of PDEs · Mathematics 2024-07-23 Clément Cancès , Jean Cauvin-Vila , Claire Chainais-Hillairet , Virginie Ehrlacher

Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical concentrations and cell biology. We present a space-time…

Analysis of PDEs · Mathematics 2022-05-19 Marcel Braukhoff , Ilaria Perugia , Paul Stocker

We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical…

Numerical Analysis · Mathematics 2021-07-15 Francesco Bonaldi , Konstantin Brenner , Jérôme Droniou , Roland Masson

Predicting the flow of non-Newtonian fluids in porous structure is still a challenging issue due to the interplay betwen the microscopic disorder and the non-linear rheology. In this letter, we study the case of an yield stress fluid in a…

Soft Condensed Matter · Physics 2019-06-26 Chen Liu , Andrea De Luca , Alberto Rosso , Laurent Talon

Excess pore pressure in granular--fluid mixtures can transiently suppress frictional contacts and dramatically enhance flow mobility, yet its evolution is commonly modeled using constant effective diffusivities. Here we show that the…

Soft Condensed Matter · Physics 2026-04-21 Eric C. P. Breard , Claudia Elijas Parra , Mattia de' Michieli Vitturi

The global-in-time existence of renormalized solutions to reaction-cross-diffu-sion systems for an arbitrary number of variables in bounded domains with no-flux boundary conditions is proved. The cross-diffusion part describes the…

Analysis of PDEs · Mathematics 2017-11-07 Xiuqing Chen , Ansgar Jüngel

We consider the initial-boundary value problem of a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities in a bounded domain $\Omega\subset\mathbb{R}^3$. Our first aim is to study…

Analysis of PDEs · Mathematics 2026-03-30 Harald Garcke , Maoyin Lv , Hao Wu

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…

Computational Physics · Physics 2019-10-02 Abay M. Kassa , Kundan Kumar , Sarah E. Gasda , Florin A. Radu

We study the problem of the transformation of a given reactant species into an immiscible product species, as they flow through a chemically active porous medium. We derive the equation governing the evolution of the volume fraction of the…

Fluid Dynamics · Physics 2015-01-06 Alexandre Darmon , Michael Benzaquen , Thomas Salez , Olivier Dauchot

The following paper presents two simulation strategies for compressible two-phase or multicomponent flows. One is a full non-equilibrium model in which the pressure and velocity are driven towards the equilibrium at interfaces by numerical…

Computational Physics · Physics 2021-08-13 Rémi Abgrall , Paola Bacigaluppi , Barbara Re

This paper study the two--phase problem for the forward-backward parabolic equation with diffusion function of cubic type. Existence and uniqueness for these kind of problems were obtained in literature in the case in which the phases are…

Analysis of PDEs · Mathematics 2019-07-25 Andrea Terracina

In this paper we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that individuals avoid collisions by sidestepping, which is encoded…

Analysis of PDEs · Mathematics 2017-04-20 Sabine Hittmeir , Helene Ranetbauer , Christian Schmeiser , Marie-Therese Wolfram

By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…

Soft Condensed Matter · Physics 2016-08-31 R. M. L. Evans , W. C. K. Poon