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In this paper we report on 2D numerical simulations concerning linear and nonlinear evolution of surface-tension-driven instability in two-fluid systems heated from below using classical and phase-field models. In the phase-field formalism,…

Pattern Formation and Solitons · Physics 2015-06-26 Rodica Borcia , Domnic Merkt , Michael Bestehorn

The paper studies an Allen-Cahn-type equation defined on a time-dependent surface as a model of phase separation with order-disorder transition in a thin material layer. By a formal inner-outer expansion, it is shown that the limiting…

Numerical Analysis · Mathematics 2021-05-27 Maxim Olshanskii , Xianmin Xu , Vladimir Yushutin

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…

Analysis of PDEs · Mathematics 2014-01-15 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

We investigate a family of phase field models for simulating dendritic growth of a pure supercooled substance. The central object of interest is the reaction term in the Allen-Cahn equation, which is responsible for spatial distribution of…

Computational Physics · Physics 2021-07-19 Pavel Strachota , Aleš Wodecki , Michal Beneš

In this supplementary paper we present some details on the solid-liquid interface detection, the deduction of the non-equilibrium free energy, the analysis of the granular temperature and energy per mode, a validation of the small slope…

Soft Condensed Matter · Physics 2013-04-10 Li-Hua Luu , Gustavo Castillo , Nicolás Mujica , Rodrigo Soto

This paper proposes a new variational model by integrating the Allen-Cahn term with a local binary fitting energy term for segmenting images with intensity inhomogeneity and noise. An inhomogeneous graph Laplacian initialization method…

Numerical Analysis · Mathematics 2021-09-24 Chaoyu liu , Zhonghua Qiao , Qian Zhang

In this paper a general multi-phase-field model is presented which is an extension and modification of the model proposed by Folch and Plapp for three phase fields [R. Folch and M. Plapp, Phys. Rev. E 72 011602 (2005)] to the arbitrary…

Materials Science · Physics 2013-06-07 E. Pogorelov , J. Kundin , H. Emmerich

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

A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by…

Numerical Analysis · Mathematics 2020-12-23 Bingquan Ji , Hong-lin Liao , Yuezheng Gong , Luming Zhang

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

Based on the idea of maintaining physical diffuse interface kinetics, enhancing interfacial diffusivity has recently provided a new direction for quantitative phase-field simulation at microstructural length and time scale. Establishing a…

Materials Science · Physics 2024-05-21 Yue Li , Lei Wang , Junjie Li , Jincheng Wang , Zhijun Wang

The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse…

Materials Science · Physics 2024-05-31 Chuanqi Zhu , Yuichiro Koizumi

We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An (essentially) unconditionally energy-stable…

The Cahn-Hilliard equation is one of the most common models to describe phase separation processes in mixtures of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…

Numerical Analysis · Mathematics 2023-01-23 Stefan Metzger

We present an adaptive variational procedure for unstructured meshes to capture fluid-fluid interfaces in two-phase flows. The two phases are modeled by the phase-field finite element formulation, which involves the conservative Allen-Cahn…

Fluid Dynamics · Physics 2018-07-05 Vaibhav Joshi , Rajeev K. Jaiman

We consider sharp interface asymptotics for a phase field model of two phase near spherical biomembranes involving a coupling between the local mean curvature and the local composition proposed by the first and second authors. The model is…

Analysis of PDEs · Mathematics 2020-12-24 Charles M. Elliott , Luke Hatcher , Björn Stinner

We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre's theorem and unconditional…

Statistical Mechanics · Physics 2007-05-23 Benjamin P. Vollmayr-Lee , Andrew D. Rutenberg

Phase-field equations, mostly solved numerically, are known for capturing the mesoscale microstructural evolution of a material. However, such numerical solvers are computationally expensive as it needs to generate fine mesh systems to…

Computational Engineering, Finance, and Science · Computer Science 2025-07-28 Gaijinliu Gangmei , Santu Rana , Bernard Rolfe , Kishalay Mitra , Saswata Bhattacharyya

Solid/liquid interfaces control various processes of technological relevance in the process industry and many fundamental physicochemical phenomena. This work examines the link between the atomistic description of mass transfer at…

Soft Condensed Matter · Physics 2021-09-07 Aaron R Finney , Matteo Salvalaglio

Over the past few decades, numerous N-phase incompressible diffuse-interface flow models with non-matching densities have been proposed. Despite aiming to describe the same physics, these models are generally distinct, and an overarching…

Fluid Dynamics · Physics 2025-04-01 M. F. P. ten Eikelder