相关论文: A Hele-Shaw-Cahn-Hilliard model for incompressible…
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…
Diffuse-interface theory provides a foundation for the modeling and simulation of microstructure evolution in a very wide range of materials, and for the tracking/capturing of dynamic interfaces between different materials on larger scales.…
The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn-Hilliard Volume-of-Fluid model to capture the dynamics of the air-sea interface at geophysically relevant Reynolds numbers. It…
Using thermodynamic and variational principles we examine a basic phase field model for a mixture of two incompressible fluids in strongly perforated domains. With the help of the multiple scale method with drift and our recently introduced…
We conduct a theoretical study of a two-phase-fluid-structure interaction problem in which air is driven at constant volume flux into a liquid-filled Hele-Shaw channel whose upper boundary is an elastic sheet. A depth-averaged model in the…
The paper is devoted to the simulation of maritime two-phase flows of air and water. Emphasis is put on an extension of the classical Volume-of-Fluid (VoF) method by a diffusive contribution derived from a Cahn-Hilliard (CH) model and its…
We present a technique to perform interface-resolved simulations of complex breakup dynamics in two-phase flows using the Cahn-Hilliard Navier-Stokes equations. The method dynamically decreases the interface thickness parameter in relevant…
The pinch-off dynamics of a liquid thread has been studied through numerical simulations and theoretical analysis. Occurring at small length scales, the pinch-off dynamics admits similarity solutions that can be classified into the Stokes…
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…
We study a diffuse-interface model that describes the dynamics of two-phase incompressible flows driven by the thermo-induced Marangoni effect. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity, the…
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…
Traditional mathematical models of Hele--Shaw flow consider the injection (or withdrawal) of an air bubble into (or from) an infinite body of viscous fluid. The most commonly studied feature of such a model is how the Saffman-Taylor…
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.…
We study a Cahn--Hilliard two-phase model describing the flow of two viscoelastoplastic fluids, which arises in geodynamics. A phase-field variable indicates the proportional distribution of the two fluids in the mixture. The motion of the…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
We consider the two-phase dynamics of two incompressible and immiscible fluids. As a mathematical model we rely on the Navier-Stokes-Cahn-Hilliard system that belongs to the class of diffuse-interface models. Solutions of the…
In this paper we present PDE and finite element analyses for a system of partial differential equations (PDEs) consisting of the Darcy equation and the Cahn-Hilliard equation, which arises as a diffuse interface model for the two phase…
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…
This paper is devoted to the global well-posedness of two Diffuse Interface systems modeling the motion of an incompressible two-phase fluid mixture in presence of capillarity effects in a bounded smooth domain $\Omega\subset \mathbb{R}^d$,…
We consider two-phase fluid deformable surfaces as model systems for biomembranes. Such surfaces are modeled by incompressible surface Navier-Stokes-Cahn-Hilliard-like equations with bending forces. We derive this model using the…