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Related papers: Phase-Field Modeling of Two-Phase Flows: A Project…

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A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard…

Analysis of PDEs · Mathematics 2013-01-14 Sergio Frigeri , Maurizio Grasselli , Pavel Krejčí

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

A diffuse-interface model that describes the dynamics of nonhomogeneous incompressible two-phase viscous flows is investigated in a bounded smooth domain in ${\mathbb R}^3.$ The dynamics of the state variables is described by the…

Analysis of PDEs · Mathematics 2024-09-19 Nie Rui , Fang Li , Guo Zhenhua

We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effect. The PDE system couples a Navier-Stokes equation for the fluid velocity, a convective Cahn-Hilliard equation for the…

Analysis of PDEs · Mathematics 2020-02-04 Jingning He

In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the Navier--Stokes equations, nonlinearly…

Analysis of PDEs · Mathematics 2018-01-09 S. Frigeri , M. Grasselli , J. Sprekels

The dripping-to-jetting transitions in coaxial flows have been experimentally well studied for systems of high interfacial tension, where the capillary number of the outer fluid and the Weber number of the inner fluid are in control. Recent…

Fluid Dynamics · Physics 2023-07-17 Fukeng Huang , Weizhu Bao , Tiezheng Qian

We study a thermodynamically consistent phase field model for binary mixtures of micropolar fluids, i.e., fluids exhibiting internal rotations. Furnishing with classical no-slip, no-spin and no-flux boundary conditions, in a smooth and…

Analysis of PDEs · Mathematics 2025-05-30 Kin Shing Chan , Kei Fong Lam

In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…

Numerical Analysis · Mathematics 2020-11-02 Chen Liu , Deep Ray , Christopher Thiele , Lu Lin , Beatrice Riviere

We propose a novel second order in time numerical scheme for Cahn-Hilliard-Navier- Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection…

Numerical Analysis · Mathematics 2016-11-25 Daozhi Han , Xiaoming Wang

The large deformations and break up of circular 2D liquid patches in a high Reynolds number (Re=1000) gas flow are investigated numerically. The 2D, plane flow Navier--Stokes equations are directly solved with explicit tracking of the…

chao-dyn · Physics 2009-10-28 S. Zaleski , Jie Li , S. Succi

We develop a decoupled, first-order, fully discrete, energy-stable scheme for the Cahn-Hilliard-Navier-Stokes equations. This scheme calculates the Cahn-Hilliard and Navier-Stokes equations separately, thus effectively decoupling the entire…

Numerical Analysis · Mathematics 2025-06-25 Haijun Gao , Xi Li , Minfu Feng

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the…

Numerical Analysis · Mathematics 2016-06-09 Amanda E. Diegel , Cheng Wang , Xiaoming Wang , Steven M. Wise

We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the…

Numerical Analysis · Mathematics 2024-05-09 Jiajie Li , Shengfeng Zhu

The Phase-Field Method (PFM) is employed to simulate two-phase flows with the fully-coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations governing the temporal evolution. The methodology minimizes the total energy functional, accounting for…

We propose a variant of the $\theta$-scheme for diffuse interface models for two-phase flow, together with three new linearization techniques for the surface tension. These involve either additional stabilizing force terms, or a fully…

Numerical Analysis · Mathematics 2014-03-05 Sebastian Aland

We investigate the sharp interface limit of a diffuse interface system that couples the Allen--Cahn equation with the instationary Navier--Stokes system in a bounded domain in $\mathbb{R}^d$ with $d \in \{2,3\}$. This model is used to…

Analysis of PDEs · Mathematics 2022-05-17 Sebastian Hensel , Yuning Liu

We analyze a diffuse interface model that describes the dynamics of incompressible viscous two-phase flows, incorporating mechanisms such as chemotaxis, active transport, and long-range interactions of Oono's type. The evolution system…

Analysis of PDEs · Mathematics 2025-10-28 Jingning He , Hao Wu

In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier-Stokes equations in the two fluid phases, connected by…

Numerical Analysis · Mathematics 2026-02-11 Harald Garcke , Robert Nürnberg , Dennis Trautwein

In this paper, we develop a novel phase-field model for fluid-structure interaction (FSI), that is capable to handle very large deformations as well as topology changes like contact of the solid to the domain boundary. The model is based on…

Computational Physics · Physics 2023-05-03 Dominic Mokbel , Helmut Abels , Sebastian Aland

We propose and analyze two novel decoupled numerical schemes for solving the Cahn-Hilliard-Stokes-Darcy (CHSD) model for two-phase flows in karstic geometry. In the first numerical scheme, we explore a fractional step method (operator…

Numerical Analysis · Mathematics 2016-10-19 Wenbin Chen , Daozhi Han , Xiaoming Wang