Related papers: Gradient flow dynamics of two-phase biomembranes: …
In this paper, we present a numerical scheme for the diffuse-interface model in [Abels, Garcke, Gr\"un, M3AS 22(3), 2012] for two-phase flow of immiscible, incompressible fluids. As that model is in particular consistent with…
Motivated by solid-solid phase transitions in elastic thin films, we perform a Gamma-convergence analysis for a singularly perturbed energy describing second order phase transitions in a domain of vanishing thickness. Under a two-wells…
In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter $\epsilon$, representing the interface thickness between the tumorous and non tumorous cells,…
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…
In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward…
In this paper, we introduce a novel way to represent the interface for two-phase flows with phase change. We combine a level-set method with a Cartesian embedded boundary method and take advantage of both. This is part of an effort to…
The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework proposed in (C M Elliott, T Ranner, IMA J Num Anal, 41:3,…
The effect of rigid surfaces on the dynamics of thin liquid films which are amenable to the lubrication approximation is considered. It is shown that the Helfrich energy of the layer gives rise to additional terms in the time-evolution…
Correctly formulated continuum models for lipid-bilayer membranes present a significant challenge to computational mechanics. In particular, the mid-surface behavior is that of a 2-dimensional fluid, while the membrane resists bending much…
We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right…
Having a finite interfacial thickness, the phase-field models supply a way to model the fluid interfaces, which allows the calculations of the interface movements and deformations on the fixed grids. Such modeling is applied to the…
In this paper we propose a novel and general approach to design semi-implicit methods for the simulation of fluid-structure interaction problems in a fully Eulerian framework. In order to properly present the new method, we focus on the…
We consider fully discrete numerical approximations for axisymmetric Willmore flow that are unconditionally stable and work reliably without remeshing. We restrict our attention to surfaces without boundary, but allow for spontaneous…
We consider a sharp interface formulation for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling. The flow is characterized by a cluster of surfaces evolving such that the total surface energy plus a weighted sum…
Reductions of the self-consistent mean field theory model of amphiphilic molecules in solvent can lead to a singular family of functionalized Cahn-Hilliard energies. We modify these energies, mollifying the singularities to stabilize the…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
Optimal-order uniform-in-time $H^1$-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic…
The evolution of the interface between two ideal dielectric liquids in a strong vertical electric field is studied. It is found that a particular flow regime, for which the velocity potential and the electric field potential are linearly…
A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the…
A thermodynamically consistent phase-field model is introduced for simulating motion and shape transformation of vesicles under flow conditions. In particular, a general slip boundary condition is used to describe the interaction between…