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Related papers: Cahn-Hilliard on Surfaces: A Numerical Study

200 papers

The mathematical analysis of diffuse-interface models for multiphase flows has attracted significant attention due to their ability to capture complex interfacial dynamics, including curvature effects, within a unified, energetically…

Analysis of PDEs · Mathematics 2025-09-25 Pierluigi Colli , Gianni Gilardi , Andrea Signori , Jürgen Sprekels

We consider the identifiability and stable numerical estimation of multiple parameters in a Cahn-Hilliard model for phase separation. Spatially resolved measurements of the phase fraction are assumed to be accessible, with which the…

Numerical Analysis · Mathematics 2023-05-03 Aaron Brunk , Herbert Egger , Oliver Habrich

The paper presents a complete research cycle comprising continuum-based modeling, computational framework development, and validation setup to predict phase separation and surface hydrodynamics in lipid bilayer membranes. We starting with…

Numerical Analysis · Mathematics 2025-10-14 Maxim Olshanskii , Annalisa Quaini

A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for the space discretization:the scalar unknowns are located in…

Numerical Analysis · Mathematics 2021-11-19 R Herbin , J. -C Latché , Y Nasseri , N Therme

This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…

Numerical Analysis · Mathematics 2021-09-08 John Jomo , Oguz Oztoprak , Frits de Prenter , Nils Zander , Stefan Kollmannsberger , Ernst Rank

We derive a new effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by 4-th order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly…

Mathematical Physics · Physics 2013-10-02 Markus Schmuck , Marc Pradas , Greg A. Pavliotis , Serafim Kalliadasis

In this paper, we design, analyze and implement efficient time parallel method for a class of fourth order time-dependent partial differential equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard (CH) equation and the…

Numerical Analysis · Mathematics 2023-04-28 Gobinda Garai , Bankim C. Mandal

The paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system. The operators appearing in the system equations were fractional…

Analysis of PDEs · Mathematics 2018-12-17 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

Behavior of two-time autocorrelation during the phase separation in solid binary mixtures are studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via…

Statistical Mechanics · Physics 2015-09-02 Jiarul Midya , Suman Majumder , Subir K. Das

The isentropic compressible Cahn-Hilliard-Navier-Stokes equations is a system of fourth-order partial differential equations that model the evolution of some binary fluids under convection. The purpose of this paper is the design of…

Numerical Analysis · Mathematics 2024-04-02 Pep Mulet

A fully discrete semi-convex-splitting finite-element scheme with stabilization for a Cahn-Hilliard cross-diffusion system is analyzed. The system consists of parabolic fourth-order equations for the volume fraction of the fiber phase and…

Numerical Analysis · Mathematics 2024-06-05 Ansgar Jüngel , Boyi Wang

In this paper we study the optimal control of an initial-boundary value problem for the classical nonviscous Cahn-Hilliard system with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive…

Optimization and Control · Mathematics 2024-06-12 Pierluigi Colli , Jürgen Sprekels

An implicit variable-step BDF2 scheme is established for solving the space fractional Cahn-Hilliard equation, involving the fractional Laplacian, derived from a gradient flow in the negative order Sobolev space $H^{-\alpha}$,…

Numerical Analysis · Mathematics 2023-06-26 Xuan Zhao , Zhongqin Xue

This article is concerned with a gradient-flow approach to a Cahn-Hilliard model for viscoelastic phase separation introduced by Zhou et al. (Phys. Rev. E, 2006) in its variant with constant mobility. By means of time-incremental…

Analysis of PDEs · Mathematics 2025-08-22 Moritz Immanuel Gau , Katharina Hopf

We consider a diffuse interface model for phase separation of an isothermal incompressible binary fluid in a Brinkman porous medium. The coupled system consists of a convective Cahn-Hilliard equation for the phase field $\phi$, i.e., the…

Analysis of PDEs · Mathematics 2014-08-15 Stefano Bosia , Monica Conti , Maurizio Grasselli

Degenerate Cahn-Hilliard phase-field models provide a robust approximation of surface-diffusion-driven interface motion without explicit front tracking. In computations, however, the geometric volume enclosed by the interface -- the region…

Numerical Analysis · Mathematics 2026-02-03 Josef Musil

In this paper we study a non-local Cahn-Hilliard equation with singular single-well potential and degenerate mobility. This results as a particular case of a more general model derived for a binary, saturated, closed and incompressible…

Analysis of PDEs · Mathematics 2023-06-29 Abramo Agosti , Elisabetta Rocca , Luca Scarpa

We present and analyze an unconditionally energy stable and convergent finite difference scheme for the Functionalized Cahn-Hilliard equation. One key difficulty associated with the energy stability is based on the fact that one nonlinear…

Numerical Analysis · Mathematics 2016-10-11 Wenqiang Feng , Zhen Guan , John Lowengrub , Cheng Wang , Steven M. Wise

In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the…

Numerical Analysis · Mathematics 2021-12-09 Yali Gao , Daozhi Han , Xiaoming He , Ulrich Rüde

This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…

Numerical Analysis · Mathematics 2023-07-06 R. Altmann , C. Zimmer