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A new method for interface tracking is presented. The interface representation, based on domain decomposition, provides the interface location explicitly, yet is Eulerian. This allows for well established finite difference methods on…

Fluid Dynamics · Physics 2013-02-20 Dag Lindbo , Anna-Karin Tornberg

In this work we introduce the development of a three--phase incompressible Navier--Stokes/Cahn--Hilliard numerical method to simulate three--phase flows, present in many industrial operations. The numerical method is then applied to…

We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…

Numerical Analysis · Mathematics 2023-06-21 Harald Garcke , Robert Nürnberg , Quan Zhao

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this…

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…

Analysis of PDEs · Mathematics 2014-01-15 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

We consider a diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids. This model consists of the Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation.…

Analysis of PDEs · Mathematics 2015-09-11 Sergio Frigeri , Ciprian G. Gal , Maurizio Grasselli

The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transition is taken into account. To this end, two…

Analysis of PDEs · Mathematics 2025-05-09 Helmut Abels , Harald Garcke , Julia Wittmann

We derive and analyze a new diffuse interface model for incompressible, viscous fluid mixtures with bulk-surface interaction. Our system consists of a Navier--Stokes--Cahn--Hilliard model in the bulk that is coupled to a surface…

Analysis of PDEs · Mathematics 2025-09-16 Patrik Knopf , Jonas Stange

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and…

Computational Physics · Physics 2015-05-20 Kazuyasu Sugiyama , Satoshi Ii , Shintaro Takeuchi , Shu Takagi , Yoichiro Matsumoto

Using a fixed Eulerian mesh, the phase-field method has been successfully utilized for a broad range of moving boundary problems involving multiphase fluids and single-phase fluid-structure interaction. Nevertheless, multiphase fluids…

Fluid Dynamics · Physics 2024-02-19 Xiaoyu Mao , Rajeev Jaiman

In this article, we study the behavior of the Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard diffuse-interface model for binary-fluid flows, as the diffuse-interface thickness passes to zero. We consider this so-called sharp-interface…

Numerical Analysis · Mathematics 2023-01-05 T. H. B. Demont , S. K. F. Stoter , E. H. van Brummelen

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…

Analysis of PDEs · Mathematics 2020-10-14 Helmut Abels , Josef Weber

We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…

Numerical Analysis · Mathematics 2022-01-19 Nils Margenberg , Thomas Richter

A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary-fluids and…

Analysis of PDEs · Mathematics 2011-02-22 Pierluigi Colli , Sergio Frigeri , Maurizio Grasselli

In this paper, we study a diffuse interface model for two-phase immiscible flows coupled by Navier-Stokes equations and mass-conserving Allen-Cahn equations. The contact line (the intersection of the fluid-fluid interface with the solid…

Analysis of PDEs · Mathematics 2025-03-12 Yinghua Li , Yuanxiang Yan , Xijun Yin

We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…

Numerical Analysis · Mathematics 2023-09-12 Harald Garcke , Robert Nürnberg , Quan Zhao

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model…

Analysis of PDEs · Mathematics 2015-06-03 Helmut Abels , Daniel Depner , Harald Garcke

We study a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids coupling the Navier--Stokes system with a convective nonlocal Cahn--Hilliard equation in two dimensions of space. We apply recently proved…

Analysis of PDEs · Mathematics 2014-11-07 Sergio Frigeri , Elisabetta Rocca , Jürgen Sprekels

We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows influenced by interactions with a soluble chemical substance, encompassing the chemotaxis effect, mass transport, and reactions. In the…

Analysis of PDEs · Mathematics 2026-01-13 Andrea Giorgini , Jingning He , Hao Wu

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring…

Numerical Analysis · Mathematics 2018-10-30 Oliver R. A. Dunbar , Kei Fong Lam , Bjorn Stinner