On different implementations of boundary conditions in the meshless RBF-FD method for phase-field modelling of dendritic solidification

Dobravec, Tadej (author), Mavrič, Boštjan (author), Šarler, Božidar (author)

Dendritic morphology is one of the most common microstructures in solidifying metallic materials. The phase-field method represents one of the most suitable approaches for modelling the evolution of dendritic morphology. In this paper, the meshless RBF-FD method and forward Euler scheme are used to solve the partial differential equations arising from the phase-field model for dendritic growth. We consider the growth of a single dendrite into a supercooled pure melt. On the computational domain's surfaces, we apply symmetric boundary conditions. Special care has to be taken in the RBF-FD method to satisfy boundary conditions accurately. In this paper, we test four different implementations of boundary conditions. In the first one, the boundary conditions are incorporated when constructing an interpolation problem in local support domains containing boundary nodes. In the second one, the interpolation problem in the local support domains does not consider boundary conditions, which are satisfied by solving a system of linear equations for values in all boundary nodes at each time step. The third one complements the second one with the use of ghost nodes. The fourth implementation is an alternative one, where the values in ghost nodes are determined by direct mirroring. The accuracy and computational efficiency of all four implementations are compared. We discuss the advantages and disadvantages of each implementation. We show that using ghost nodes is recommended for implementing Neumann boundary conditions in the RBF-FD method.

• Language: English
• Keywords: dendritic growth, phase-field method, meshless methods, boundary conditions
• Typology: 1.08 - Published Scientific Conference Contribution
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 6 str.
• Numbering: Vol. 2766, art. 012162
• PID: 20.500.12556/RUL-158329
• UDC: 519.62
• ISSN on article: 1742-6596
• DOI: 10.1088/1742-6596/2766/1/012162
• COBISS.SI-ID: 197919747
• Publication date in RUL: 06.06.2024

DOBRAVEC, Tadej, MAVRIČ, Boštjan and ŠARLER, Božidar, 2024, On different implementations of boundary conditions in the meshless RBF-FD method for phase-field modelling of dendritic solidification. In : Eurotherm 2024 [online]. Published Scientific Conference Contribution. 2024. [Accessed 1 June 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=158329

Record is a part of a proceedings

• Title: Eurotherm 2024
• COBISS.SI-ID: 197654787

Record is a part of a journal

• Title: Journal of physics. Conference series
• Publisher: Institute of Physics Publishing
• ISSN: 1742-6596
• COBISS.SI-ID: 2035044

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: dendritska rast, metoda faznega polja, brezmrežne metode, robni pogoji