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Mathematics
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Scientific Computing for Phase-Field Models
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Scientific Computing for Phase-Field Models

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 20 September 2025 | Viewed by 130

Special Issue Editors

Prof. Dr. Junseok Kim

E-Mail Website
Guest Editor
Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
Interests: computational mathematics; scientific computing; numerical analysis; mathematical physics; computational biology; computational finance; computer simulation; mathematical modeling
Special Issues, Collections and Topics in MDPI journals
Dr. Hyundong Kim

E-Mail Website
Guest Editor
Department of Mathematics and Physics, Gangneung-Wonju National University, Gangneung 25457, Republic of Korea
Interests: phase-field model; PDE on surface; mathematical biology; computational finance; scientific computing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Phase-field models are a powerful mathematical and computational approach used to simulate the behavior of interfaces and boundaries in complex systems without the need for explicitly tracking their positions. The phase-field models have become crucial tools for understanding and predicting the evolution of microstructures in materials, fluid flows, and other phenomena involving phase changes or morphological transformations.

The purpose of this Special Issue is to highlight the latest research on the developments and applications of 'scientific computing for phase-field models'.

The scope of this Special Issue encompasses a wide range of topics related to phase-field models, including, but not limited to, the following:

  • Phase-field models;
  • Phase-field equations solver on curved surfaces;
  • Phase-field model and Navier–Stokes systems;
  • Fourier spectral method for phase-field models;
  • Multigrid method;
  • Finite difference method;
  • Operator splitting method;
  • Topological optimization;
  • Mesh generation algorithm.

Prof. Dr. Junseok Kim
Dr. Hyundong Kim
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • phase-field models
  • phase-field equations
  • finite difference method
  • scientific computing
  • topological optimization
  • mesh generation algorithm

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Published Papers (1 paper)

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Research

17 pages, 1659 KiB  
Article
Efficient Phase-Field Modeling of Quasi-Static and Dynamic Crack Propagation Under Mechanical and Thermal Loadings
by Lotfi Ben Said, Hamdi Hentati, Mohamed Turki, Alaa Chabir, Sattam Alharbi and Mohamed Haddar
Mathematics 2025, 13(11), 1742; https://doi.org/10.3390/math13111742 (registering DOI) - 24 May 2025
Abstract
The main objective of this work was to model the failure mechanisms of brittle materials subjected to thermal and mechanical loads. A diffusive representation of the crack topology provides the basis for the regularized kinematic framework used. With a smooth transition from the [...] Read more.
The main objective of this work was to model the failure mechanisms of brittle materials subjected to thermal and mechanical loads. A diffusive representation of the crack topology provides the basis for the regularized kinematic framework used. With a smooth transition from the undamaged to the fully damaged state, the fracture surface was roughly represented as a diffusive field. By integrating a staggered scheme and spectral decomposition, the variational formulation was used after being mathematically written and developed. Its effectiveness was analyzed using extensive benchmark tests, demonstrating the effectiveness of the phase-field model in modeling the behavior of brittle materials. This proposed approach was experimentally tested through the examination of crack propagation paths in brittle materials that were subjected to variable mechanical and thermal loads. This work focused on the integration of a spectral decomposition-based phase-field model with thermo-mechanical coupling for dynamic fracture, supported by benchmark validation and the comparative assessment of energy decomposition strategies. The results highlight the accuracy and robustness of numerical and experimental methodologies proposed to model fracture mechanics in brittle materials subjected to complex loading conditions. Full article
(This article belongs to the Special Issue Scientific Computing for Phase-Field Models)
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