| Title: | Adaptive hyperviscosity stabilisation for the RBF-FD method in solving advection-dominated transport equations |
|---|
| Authors: | ID Rot, Miha, Institut "Jožef Stefan" (Author)
ID Vaupotič, Žiga, Institut "Jožef Stefan" (Author)
ID Kolar-Požun, Andrej, Institut "Jožef Stefan" (Author)
ID Kosec, Gregor, Institut "Jožef Stefan" (Author) |
|---|
| Files: |  URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0021999126001786?via%3Dihub
 PDF - Presentation file, download (4,21 MB)
MD5: 30FB813656680264F2E19D7EC7EDFC07
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IJS - Jožef Stefan Institute
|
|---|
| Abstract: | 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. |
|---|
| Keywords: | meshless methods, hyperviscosity, stabilisation scheme, advection, Burgers' equation |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Submitted for review: | 29.10.2025 |
|---|
| Article acceptance date: | 05.03.2026 |
|---|
| Publication date: | 08.03.2026 |
|---|
| Publisher: | Elsevier |
|---|
| Year of publishing: | 2026 |
|---|
| Number of pages: | str. 1-18 |
|---|
| Numbering: | Vol. 557, [article no.] 114828 |
|---|
| Source: | Nizozemska |
|---|
| PID: | 20.500.12556/DiRROS-28569  |
|---|
| UDC: | 51 |
|---|
| ISSN on article: | 1090-2716 |
|---|
| DOI: | 10.1016/j.jcp.2026.114828 |
|---|
| COBISS.SI-ID: | 272762115 |
|---|
| Copyright: | © 2026 The Author(s). |
|---|
| Note: | Nasl. z nasl. zaslona;
Soavtorji: Žiga Vaupotič, Andrej Kolar-Požun, Gregor Kosec;
Opis vira z dne 24. 3. 2026;
|
|---|
| Publication date in DiRROS: | 24.03.2026 |
|---|
| Views: | 133 |
|---|
| Downloads: | 70 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
