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We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is…

Analysis of PDEs · Mathematics 2024-09-26 Markus Gahn , Maria Neuss-Radu

Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological…

In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…

Analysis of PDEs · Mathematics 2025-03-06 Yinghua Li , Wenlin Ye

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…

Fluid Dynamics · Physics 2011-04-08 H. Abels , H. Garcke , G. Grün

In this paper, we introduce an interfacial profile-preserving approach for phase field modeling for simulating incompressible two-phase flows. While the advective Cahn-Hilliard equation effectively captures the topological evolution of…

Fluid Dynamics · Physics 2023-10-03 Haohao Hao , Xiangwei Li , Chenglin Jiang , Huanshu Tan

Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in time in an…

Numerical Analysis · Mathematics 2020-07-13 Manuela Bastidas , Carina Bringedal , Iuliu Sorin Pop

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the…

Analysis of PDEs · Mathematics 2021-10-28 Yazhou Chen , Hakho Hong , Xiaoding Shi

We show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2026-05-01 Helmut Abels , Jonas Haselböck

Over the past few decades, numerous N-phase incompressible diffuse-interface flow models with non-matching densities have been proposed. Despite aiming to describe the same physics, these models are generally distinct, and an overarching…

Fluid Dynamics · Physics 2025-04-01 M. F. P. ten Eikelder

Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are…

Fluid Dynamics · Physics 2013-03-12 Harald Garcke , Kei Fong Lam , Björn Stinner

Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical…

Fluid Dynamics · Physics 2019-06-10 Baofang Song , Carlos Plana , Jose M. Lopez , Marc Avila

We consider the process of convective dissolution in homogeneous and isotropic porous media. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is…

Fluid Dynamics · Physics 2024-08-02 Marco De Paoli , Christopher J. Howland , Roberto Verzicco , Detlef Lohse

We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…

Analysis of PDEs · Mathematics 2025-10-14 Marcel Zodji

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

We consider the homogenisation of a coupled Stokes flow and advection-reaction-diffusion problem in a perforated domain with an evolving microstructure of size $\varepsilon$. Reactions at the boundaries of the microscopic interfaces lead to…

Analysis of PDEs · Mathematics 2024-04-05 Markus Gahn , Malte A. Peter , Iuliu Sorin Pop , David Wiedemann

The Cahn-Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not grow larger than a certain size. This phenomenon has been…

Analysis of PDEs · Mathematics 2025-11-07 Harald Garcke , Kei Fong Lam , Robert Nürnberg , Andrea Signori

Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn--Hilliard model on an evolving hypersurface coupled to Navier--Stokes equations on the surface…

Numerical Analysis · Mathematics 2019-11-01 John W. Barrett , Harald Garcke , Robert Nürnberg

In this paper, we consider numerical approximations of a binary fluid-surfactant phase-field model coupled with the fluid flow, in which the system is highly nonlinear that couples the incompressible Navier-Stokes equations and two…

Numerical Analysis · Mathematics 2018-04-13 Xiaofeng Yang

We consider shape and topology optimization for fluids which are governed by the Navier--Stokes equations. Shapes are modelled with the help of a phase field approach and the solid body is relaxed to be a porous medium. The phase field…

Optimization and Control · Mathematics 2015-04-27 Harald Garcke , Claudia Hecht , Michael Hinze , Christian Kahle , Kei Fong Lam

This paper presents a topology optimization approach for surface flows, which can represent the viscous and incompressible fluidic motions at the solid/liquid and liquid/vapor interfaces. The fluidic motions on such material interfaces can…

Computational Physics · Physics 2020-05-18 Yongbo Deng , Weihong Zhang , Jihong Zhu , Junqiang Bai , Zhenyu Liu , Jan G. Korvink