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

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

Abstract

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.

Keywords

dendritska rast;metoda faznega polja;brezmrežne metode;robni pogoji;dendritic growth;phase-field method;meshless methods;boundary conditions;

Data

Language:	English
Year of publishing:	2024
Typology:	1.08 - Published Scientific Conference Contribution
Organization:	UL FS - Faculty of Mechanical Engineering
UDC:	519.62
COBISS:	197919747
ISSN:	1742-6596
Views:	55
Downloads:	15
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	dendritska rast;metoda faznega polja;brezmrežne metode;robni pogoji;
Type (COBISS):	Article
Pages:	str. 1-6
Issue:	ǂVol. ǂ2766, [article no.] 012162
Chronology:	2024
DOI:	10.1088/1742-6596/2766/1/012162
ID:	24291088