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Laser-based metal processing including welding and three dimensional printing, involves localized melting of solid or granular raw material, surface tension-driven melt flow and significant evaporation of melt due to the applied very high…

Computational Engineering, Finance, and Science · Computer Science 2021-05-05 Christoph Meier , Sebastian L. Fuchs , A. John Hart , Wolfgang A. Wall

We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the…

Numerical Analysis · Mathematics 2017-01-10 Weizhu Bao , Wei Jiang , Yan Wang , Quan Zhao

We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a…

Numerical Analysis · Mathematics 2026-01-07 Louis Libat , Can Selçuk , Eric Chénier , Vincent Le Chenadec

A new phase field model is introduced, which can be viewed as nontrivial generalisation of what is known as the Caginalp model. It involves in particular nonlinear diffusion terms. By formal asymptotic analysis, it is shown that in the…

Analysis of PDEs · Mathematics 2012-01-18 Sylvie Benzoni-Gavage , Laurent Chupin , Didier Jamet , Julien Vovelle

I use the method of classical density-functional theory in the weighted-density approximation of Tarazona to investigate the phase diagram and the interface structure of a two-dimensional lattice-gas model with three phases -- vapour,…

Statistical Mechanics · Physics 2009-11-10 S. Prestipino

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…

Analysis of PDEs · Mathematics 2016-11-01 Ugur G. Abdulla

We study the one-phase one-dimensional supercooled Stefan problem with oscillatory initial conditions. In this context, the global existence of so-called physical solutions has been shown recently in [CRSF20], despite the presence of…

Probability · Mathematics 2023-11-14 Scander Mustapha , Mykhaylo Shkolnikov

We propose a numerical methodology for the simultaneous numerical simulation of four states of matter; gas, liquid, elastoplastic solids and plasma. The distinct, interacting physical processes are described by a combination of…

Computational Physics · Physics 2019-05-17 Louisa Michael , Stephen T. Millmore , Nikolaos Nikiforakis

Melting and solidification processes are often affected by natural convection of the liquid, posing a multi-physics problem involving fluid flow, convective and diffusive heat transfer, and phase-change reactions. Enthalpy methods formulate…

Computational Physics · Physics 2020-09-08 Alexander Gary Zimmerman , Julia Kowalski

In this work, a thermodynamically consistent and conservative diffuse-interface model for gas-liquid-solid multiphase flows is proposed. In this model, a novel free energy for the gas-liquid-solid multiphase flows is established according…

Fluid Dynamics · Physics 2025-04-09 Chengjie Zhan , Xi Liu , Zhenhua Chai , Baochang Shi

The inverse one-phase Stefan problem in one dimension, aimed at identifying the unknown time-dependent heat flux P(t) with a known moving boundary position s(t), is investigated. A previous study [16] attempted to reconstruct the unknown…

Numerical Analysis · Mathematics 2024-10-28 Orazbek Narbek , Samat A. Kassabek , Targyn Nauryz

We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time…

Mesoscale and Nanoscale Physics · Physics 2019-05-17 Marc Calvo-Schwarzwälder , Timothy G. Myers , Matthew G. Hennessy

The study of tree sap exudation, in which a (leafless) tree generates elevated stem pressure in response to repeated daily freeze-thaw cycles, gives rise to an interesting multi-scale problem involving heat and multiphase liquid/gas…

Analysis of PDEs · Mathematics 2018-07-24 Isabell Konrad , Malte A. Peter , John M. Stockie

Water-ice systems undergoing melting develop complex spatio-temporal interface dynamics and a non-trivial temperature field. In this contribution, we present computational aspects of a recently conducted validation study that aims at…

Fluid Dynamics · Physics 2018-01-12 K. Schüller , B. Berkels , J. Kowalski

Additive manufacturing and welding processes are highly sensitive to heat dissipation, where improper thermal management leads to residual stresses, distortions, and cracking. Existing heat transfer models, such as Rosenthal's solutions,…

Mathematical Physics · Physics 2026-04-24 Fawzi Aly , Alex Kitt , Luke Mohr

The vertical gradient freeze crystal growth process is the main technique for the production of high quality compound semiconductors that are vital for today's electronic applications. A simplified model of this process consists of two 1D…

Optimization and Control · Mathematics 2025-02-11 Stefan Ecklebe , Nicole Gehring

We introduce unconditionally stable finite element approximations for a phase field model for solidification, which take highly anisotropic surface energy and kinetic effects into account. We hence approximate Stefan problems with…

Numerical Analysis · Mathematics 2015-06-02 John W. Barrett , Harald Garcke , Robert Nürnberg

Solidification as a first order phase transition is described in the Landau theory by the same equation as tricritical phenomena. Here, the solidification or melting temperature against pressure curve is modelled to end at a tricritical…

Statistical Mechanics · Physics 2007-05-23 A. Aitta

In the present study, a consistent and conservative Phase-Field model is developed to study thermo-gas-liquid-solid flows with liquid-solid phase change. The proposed model is derived with the help of the consistency conditions and exactly…

Computational Physics · Physics 2021-11-16 Ziyang Huang , Guang Lin , Arezoo M. Ardekani

In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…

Numerical Analysis · Mathematics 2022-06-15 Yuzhe Qin , Huaxiong Huang , Yi Zhu , Chun Liu , Shixin Xu