20.500.12556/RUL-167545 A study on different implementations of Neumann boundary conditions in the meshless RBF-FD method for the phase-field modelling of dendrite growth 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. dendritic growth phase-field method Neumann boundary conditions RBF-FD ghost nodes dendritska rast metoda faznega polja RBF-FD Neumannovi robni pogoji true false true Angleški jezik Slovenski jezik Članek v reviji 2025-02-27 10:24:45 2025-02-27 10:24:51 2025-03-15 04:06:38 0000-00-00 00:00:00 2025 0 0 9 str. art. 106154 Vol. 173 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 004.94:51:621.742.4 1873-197X 10.1016/j.enganabound.2025.106154 227519491 1-s2.0-S0955799725000426-main.pdf 1-s2.0-S0955799725000426-main.pdf 1 C377B4A1FCBE4195E76A459F36458D7F b58e558562dcfeba173a3fd2628b7ef897d1569059db582f4cc05bc5ad98c655 bfbefd76-00d4-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=200693 https://www.sciencedirect.com/science/article/pii/S0955799725000426 0 ca39cf4a-f4eb-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=200173 Fakulteta za strojništvo 0 0 0