20.500.12556/DiRROS-28569 Adaptive hyperviscosity stabilisation for the RBF-FD method in solving advection-dominated transport equations This paper presents an adaptive hyperviscosity stabilisation procedure for the Radial Basis Function-generated Finite Difference (RBF-FD) method, aimed at solving linear and non-linear advection-dominated transport equations on domains without a boundary. The approach employs an equation independent algorithm that adaptively determines the hyperviscosity constant based on the spectral radius of the RBF-FD evolution matrix. The proposed procedure supports general node layouts and is not tailored for specific equations, avoiding the limitations of empirical tuning and von Neumann-based estimates. To reduce computational cost, it is shown that lower monomial augmentation in the approximation of the hyperviscosity operator can still ensure consistent stabilisation, enabling the use of smaller stencils and improving overall efficiency. A hybrid strategy employing different spline orders for the advection and hyperviscosity operators is also implemented to enhance stability. The method is evaluated on pure linear advection and non-linear Burgers’ equation, demonstrating stable performance with limited numerical dissipation. The two main contributions are: (1) a general hyperviscosity RBF-FD solution procedure demonstrated on both linear and non-linear advection-dominated problems, and (2) an in-depth analysis of the behaviour of hyperviscosity within the RBF-FD framework, addressing the interplay between key free parameters and their influence on numerical results. meshless methods hyperviscosity stabilisation scheme advection Burgers' equation brezmrežne metode hiperviskoznost Burgersova enačba true false false Elsevier Nizozemska Angleški jezik Slovenski jezik © 2026 The Author(s). Neznano 2026-03-24 10:44:43 2026-03-24 10:44:43 2026-03-27 03:44:11 0000-00-00 00:00:00 2026 0 0 Nasl. z nasl. zaslona; Soavtorji: Žiga Vaupotič, Andrej Kolar-Požun, Gregor Kosec; Opis vira z dne 24. 3. 2026; str. 1-18 Vol. 557, [article no.] 114828 Jul. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2025-10-29 2026-03-05 2026-03-08 51 1090-2716 10.1016/j.jcp.2026.114828 272762115 https://www.sciencedirect.com/science/article/pii/S0021999126001786?via%3Dihub 1 1851b6ec-2766-11f1-aa40-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=42405 RAZ_Rot_Miha_2026.pdf RAZ_Rot_Miha_2026.pdf 1 30FB813656680264F2E19D7EC7EDFC07 b452166f25eb90507418ea6a3669c5d0c8b1dce225ecfb8c0e9162b099d75e9b 810b8f76-2766-11f1-aa40-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=42406 Institut Jožef Stefan 0 0 0