English
Related papers

Related papers: A diffuse-interface approach for solid-state dewet…

200 papers

We consider the impingement of a droplet onto a wall with high impact speed. To model this process we favour a diffuse-interface concept. Precisely, we suggest a compressible Navier--Stokes--Allen--Cahn model. Basic properties of the model…

Fluid Dynamics · Physics 2019-09-30 Lukas Ostrowski , Christian Rohde

In this work, we first propose a diffuse-interface model for the freezing processes of three-phase flows in complex geometries, and the core of the model to intergratge the Navier-Stokes equations for fluid flows, a modified phase-field…

Fluid Dynamics · Physics 2025-10-22 Jiangxu Huang , Chengjie Zhan , Zhenhua Chai , Changsheng Huang

We present a non-diagonal phase field model for phase transformations with unequal but finite diffusivities in the two phases. This model allows to recover the desired boundary conditions at the interface, and especially the elimination of…

Materials Science · Physics 2017-06-28 G. Boussinot , Efim A. Brener , C. Hueter , R. Spatschek

In this paper, a diffuse-interface lattice Boltzmann method (DI-LBM) is developed for fluid-particle interaction problems. In this method, the sharp interface between the fluid and solid is replaced by a thin but nonzero thickness…

Computational Physics · Physics 2021-06-17 Jiao Liu , Changsheng Huang , Zhenhua Chai , Baochang Shi

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…

Analysis of PDEs · Mathematics 2024-01-15 Helmut Abels , Harald Garcke , Andrea Poiatti

We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…

Numerical Analysis · Mathematics 2017-03-09 Anke Böttcher , Herbert Egger

We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points/lines,…

Numerical Analysis · Mathematics 2022-11-07 Weizhu Bao , Harald Garcke , Robert Nürnberg , Quan Zhao

Motivated by the study of the electrodynamics of particles, we propose in this work an arbitrary-order discrete de Rham scheme for the treatment of elliptic problems with potential and flux jumps across a fixed interface. The scheme…

Numerical Analysis · Mathematics 2024-09-24 Daniele A. Di Pietro , Simon Mendez , Aurelio Edoardo Spadotto

In this paper, a phase-field model is introduced to describe the evolution of a deformable, self-propelled object driven by surface-tension effects. The model couples an Allen-Cahn-type equation, which distinguishes the body from the…

Analysis of PDEs · Mathematics 2026-05-20 Masaharu Nagayama , Koya Sakakibara , Keisuke Takasao

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 derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…

Analysis of PDEs · Mathematics 2023-10-25 Andrea Giorgini , Patrik Knopf

Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain…

Materials Science · Physics 2026-02-20 Maryam Khodadad , Noel Walkington , Suresh Kalyanam , Matteo Pozzi , Kaushik Dayal

This paper presents a new monolithic free-surface formulation that exhibits correct kinetic and potential energy behavior. We focus in particular on the temporal energy behavior of two-fluids flow with varying densities. Correct energy…

Numerical Analysis · Mathematics 2019-01-11 I. Akkerman , M. ten Eikelder

The link between compressible models of tissue growth and the Hele-Shaw free boundary problem of fluid mechanics has recently attracted a lot of attention. In most of these models, only repulsive forces and advection terms are taken into…

Analysis of PDEs · Mathematics 2023-05-11 Charles Elbar , Benoît Perthame , Andrea Poiatti , Jakub Skrzeczkowski

We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike $\pm$ unit…

Statistical Mechanics · Physics 2009-11-11 L. Samaj , Z. Bajnok

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and…

Soft Condensed Matter · Physics 2009-10-31 K. R. Elder , Martin Grant , Nikolas Provatas , J. M. Kosterlitz

This paper establishes a structure-preserving numerical scheme for the Cahn--Hilliard equation with degenerate mobility. First, by applying a finite volume method with upwind numerical fluxes to the degenerate Cahn--Hilliard equation…

Numerical Analysis · Mathematics 2023-03-01 Qiong-Ao Huang , Wei Jiang , Jerry Zhijian Yang , Cheng Yuan

In this work, we proposed a diffuse interface model for the dendritic growth with thermosolutal convection. In this model, the sharp boundary between the fluid and solid dendrite is replaced by a thin but nonzero thickness diffuse…

Fluid Dynamics · Physics 2023-05-17 Chengjie Zhan , Zhenhua Chai , Baochang Shi , Ping Jiang , Shaoning Geng , Dongke Sun

In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable…

Numerical Analysis · Mathematics 2016-12-05 Klaus Deckelnick , Vanessa Styles

This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…

Fluid Dynamics · Physics 2020-02-20 Darryl D. Holm , Lennon Ó Náraigh , Cesare Tronci