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The present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due…

Numerical Analysis · Computer Science 2020-10-06 Shantanu Shahane , Narayana Aluru , Placid Ferreira , Shiv G Kapoor , Surya Pratap Vanka

In this paper, we formulate a continuum theory of solidification within the context of finite-strain coupled thermoelasticity. We aim to fill a gap in the existing literature, as the existing studies on solidification typically decouple the…

Materials Science · Physics 2024-04-23 Satya Prakash Pradhan , Arash Yavari

The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…

Materials Science · Physics 2020-03-18 Amol Subhedar , Peter K. Galenko , Fathollah Varnik

We formulate a well posed interface formulation for canonical one-dimensional evaporation two-phase model problems (the Stefan and Sucking problems) commonly used to validate production codes. We focus on the interface between the vapor and…

Numerical Analysis · Mathematics 2026-04-28 Jan Nordström

A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, which it is modelled through a…

Analysis of PDEs · Mathematics 2016-09-16 Andrea N. Ceretani , Domingo A. Tarzia

The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale "stone forests" of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan…

Fluid Dynamics · Physics 2021-02-08 Jinzi Mac Huang , Michael J. Shelley , David B. Stein

In this work we introduce a new system of partial differential equations as a simplified model for the evolution of reversible martensitic transformations under thermal cycling in low hysteresis alloys. The model is developed in the context…

Analysis of PDEs · Mathematics 2018-11-20 Francesco Della Porta

This paper develops a control and estimation design for the one-phase Stefan problem. The Stefan problem represents a liquid-solid phase transition as time evolution of a temperature profile in a liquid-solid material and its moving…

Optimization and Control · Mathematics 2017-03-20 Shumon Koga , Mamadou Diagne , Miroslav Krstic

Supercooled Stefan problems describe the evolution of the boundary between the solid and liquid phases of a substance, where the liquid is assumed to be cooled below its freezing point. Following the methodology of Delarue, Nadtochiy and…

Probability · Mathematics 2022-06-15 Christa Cuchiero , Stefan Rigger , Sara Svaluto-Ferro

The present article is dedicated to the forward and backward solution of a transient one-phase Stefan problem. In the forward problem, we compute the evolution of the initial domain for a Stefan problem where the melting temperature varies…

Numerical Analysis · Mathematics 2025-12-17 Marc Dambrine , Helmut Harbrecht

The heat transfer (conductive, convective, radiative) and the related problems (the unknown phase boundary fluid/crystal, the assessment of the quality of the grown crystals) encountered in the melt and vapour growth of single crystal as…

Fluid Dynamics · Physics 2023-01-03 A. I. Zhmakin

We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface…

Numerical Analysis · Mathematics 2023-07-04 Weizhu Bao , Quan Zhao

The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…

Numerical Analysis · Computer Science 2009-09-30 G. Haikal

Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system…

Analysis of PDEs · Mathematics 2017-10-10 Helmut Abels , Harald Garcke , Josef Weber

The computer simulation of quasistationary Stefan problem has been realized. Different representations of the Laplacian growth model are considered. The main attention has been paid for the interface dynamics represented by integro…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 R. Andrushkiw , V. Gafiychuk , R. Zabrodsky

The influence of solidification on the spreading of liquids is addressed in the situation of an advancing liquid wedge on a cold substrate at $T_p < T_f$, of infinite thermal conductivity, where $T_f$ is the melting temperature. We propose…

Fluid Dynamics · Physics 2020-10-28 Rémy Herbaut , Julien Dervaux , Philippe Brunet , Laurent Royon , Laurent Limat

We consider the dynamics of an elastic continuum under large deformation but small strain. Such systems can be described by the equations of geometrically nonlinear elastodynamics in combination with the St. Venant-Kirchhoff material law.…

Systems and Control · Electrical Eng. & Systems 2024-01-31 Tobias Thoma , Paul Kotyczka , Herbert Egger

In this paper, a backstepping observer and an output feedback control law are designed for the stabilization of the one-phase Stefan problem. The present result is an improvement of the recent full state feedback backstepping controller…

Optimization and Control · Mathematics 2016-09-28 Shumon Koga , Mamadou Diagne , Miroslav Krstic

The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the…

Materials Science · Physics 2009-11-13 Luiza Angheluta , Espen Jettestuen , Joachim Mathiesen

We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…

Analysis of PDEs · Mathematics 2020-02-24 Chifaa Ghanmi , Saloua Mani-Aouadi , Faouzi Triki