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A comparison of numerical models for one-dimensional Stefan problems

Authors:

F. J. Vermolen,

S. van der ZwaagAuthors Info & Claims

Journal of Computational and Applied Mathematics, Volume 192, Issue 2

Pages 445 - 459

https://doi.org/10.1016/j.cam.2005.04.062

Published: 01 August 2006 Publication History

Abstract

In this paper, we present a critical comparison of the suitability of several numerical methods, level set, moving grid and phase field model, to address two well-known Stefan problems in phase transformation studies: melting of a pure phase and diffusional solid-state phase transformations in a binary system. Similarity solutions are applied to verify the numerical results. The comparison shows that the type of phase transformation considered determines the convenience of the numerical techniques. Finally, it is shown both numerically and analytically that the solid-solid phase transformation is a limiting case of the solid-liquid transformation.

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Fullana TLe Chenadec VSayadi T(2023)Adjoint-based optimization of two-dimensional Stefan problemsJournal of Computational Physics10.1016/j.jcp.2022.111875475:COnline publication date: 15-Feb-2023
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Bayat EEgan RBochkov DSauret AGibou F(2022)A sharp numerical method for the simulation of Stefan problems with convective effectsJournal of Computational Physics10.1016/j.jcp.2022.111627471:COnline publication date: 15-Dec-2022
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A comparison of numerical models for one-dimensional Stefan problems

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Published In

cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 192, Issue 2

1 August 2006

298 pages

ISSN:0377-0427

Issue’s Table of Contents

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 August 2006

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Cited By

Uh Zapata MItza Balam RMontalvo-Urquizo J(2023)A compact sixth-order implicit immersed interface method to solve 2D Poisson equations with discontinuitiesMathematics and Computers in Simulation10.1016/j.matcom.2023.03.012210:C(384-407)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1016/j.matcom.2023.03.012
Fullana TLe Chenadec VSayadi T(2023)Adjoint-based optimization of two-dimensional Stefan problemsJournal of Computational Physics10.1016/j.jcp.2022.111875475:COnline publication date: 15-Feb-2023
https://dl.acm.org/doi/10.1016/j.jcp.2022.111875
Bayat EEgan RBochkov DSauret AGibou F(2022)A sharp numerical method for the simulation of Stefan problems with convective effectsJournal of Computational Physics10.1016/j.jcp.2022.111627471:COnline publication date: 15-Dec-2022
https://dl.acm.org/doi/10.1016/j.jcp.2022.111627
Huang ZLin GArdekani A(2022)A consistent and conservative Phase-Field model for thermo-gas-liquid-solid flows including liquid-solid phase changeJournal of Computational Physics10.1016/j.jcp.2021.110795449:COnline publication date: 15-Jan-2022
https://dl.acm.org/doi/10.1016/j.jcp.2021.110795
Itza Balam RUh Zapata M(2022)A fourth-order compact implicit immersed interface method for 2D Poisson interface problems▪Computers & Mathematics with Applications10.1016/j.camwa.2022.06.011119:C(257-277)Online publication date: 1-Aug-2022
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Medina Dorantes FItzá Balam RUh Zapata M(2021)The immersed interface method for Helmholtz equations with degenerate diffusionMathematics and Computers in Simulation10.1016/j.matcom.2021.05.021190:C(280-302)Online publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1016/j.matcom.2021.05.021
Li MChaouki HRobert JZiegler DFafard M(2019)Numerical Simulation of Stefan Problem Coupled with Mass Transport in a Binary System Through XFEM/Level Set MethodJournal of Scientific Computing10.1007/s10915-018-0759-x78:1(145-166)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.1007/s10915-018-0759-x
Koga SKrstic M(2018)Control of Two-Phase Stefan Problem via Single Boundary Heat Input2018 IEEE Conference on Decision and Control (CDC)10.1109/CDC.2018.8619638(2914-2919)Online publication date: 17-Dec-2018
https://dl.acm.org/doi/10.1109/CDC.2018.8619638
Reutskiy S(2014)The method of approximate fundamental solutions (MAFS) for Stefan problems for the sphereApplied Mathematics and Computation10.5555/2745044.2745117227:C(648-655)Online publication date: 15-Jan-2014
https://dl.acm.org/doi/10.5555/2745044.2745117
Yoon YSong J(2014)Extended particle difference method for moving boundary problemsComputational Mechanics10.1007/s00466-014-1029-x54:3(723-743)Online publication date: 1-Sep-2014
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