| Title: | A study on different implementations of Neumann boundary conditions in the meshless RBF-FD method for the phase-field modelling of dendrite growth |
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| Authors: | ID Dobravec, Tadej (Author)
ID Mavrič, Boštjan (Author)
ID Šarler, Božidar (Author) |
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| Files: |  PDF - Presentation file, download (1,17 MB)
MD5: AF47B50D446F529F3C111551329A16C7
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0955799725000426?via%3Dihub
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMT - Institute of Metals and Technology
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| Abstract: | This paper studies and assesses different Neumann boundary conditions (BC) implementations in the radial basis function generated finite difference (RBF-FD) method. We analyse four BC implementations by solving a phase-field model for single dendrite growth in supercooled pure melts. In the first BC implementation, the BC are satisfied when constructing interpolation problems in the local support domains near the boundary. In the second one, the BC are satisfied by solving an additional system of linear equations for the field values in the boundary nodes. In the third one, we add a layer of ghost nodes to the boundary nodes; the BC are satisfied by solving an additional system of linear equations for the field values in the ghost nodes. The fourth BC implementation uses the same node distribution as the third one; since we are dealing with the symmetric BC, we set the values in the ghost nodes by direct mirroring. We analyse the influence of the size of a local support domain and the type of node distribution (regular/scattered) on the accuracy. We show that using ghost nodes is recommended to consider Neumann BC in the RBF-FD method accurately when solving phase-field models for dendritic growth. |
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| Keywords: | dendritic growth, phase-field method, Neumann boundary conditions |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.04.2025 |
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| Publisher: | Elsevier |
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| Year of publishing: | 2025 |
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| Number of pages: | 9 str. |
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| Numbering: | Vol. 173, [article no.] 106154 |
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| Source: | Engineering analysis with boundary elements |
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| PID: | 20.500.12556/DiRROS-22246  |
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| UDC: | 004.94:51:621.742.4 |
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| ISSN on article: | 1873-197X |
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| DOI: | 10.1016/j.enganabound.2025.106154 |
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| COBISS.SI-ID: | 227519491 |
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| Copyright: | © 2025 The Authors. Published by Elsevier Ltd. |
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| Note: | Nasl. z nasl. zaslona;
Opis vira z dne 26. 2. 2025;
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| Publication date in DiRROS: | 13.05.2025 |
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| Views: | 497 |
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| Downloads: | 312 |
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