A Third-order Conservative Semi-Lagrangian Discontinuous Galerkin Scheme For the Transport Equation on Curvilinear Unstructured Meshes
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918200482988032 |
|---|---|
| author | Cai, Xiaofeng Chen, Yibing Fu, Kunkai Pan, Liujun |
| author_facet | Cai, Xiaofeng Chen, Yibing Fu, Kunkai Pan, Liujun |
| contents | We develop a third-order conservative semi-Lagrangian discontinuous Galerkin (SLDG) scheme for solving linear transport equations on curvilinear unstructured triangular meshes, tailored for complex geometries. To ensure third-order spatial accuracy while strictly preserving mass, we develop a high-order conservative intersection-based remapping algorithm for curvilinear unstructured meshes, which enables accurate and conservative data transfer between distinct curvilinear meshes. Incorporating this algorithm, we construct a non-splitting high-order SLDG method equipped with weighted essentially non-oscillatory and positivity-preserving limiters to effectively suppress numerical oscillations and maintain solution positivity. For the linear problem, the semi-Lagrangian update enables large time stepping, yielding an explicit and efficient implementation. Rigorous numerical analysis confirms that our scheme achieves third-order accuracy in both space and time, as validated by consistent error analysis in terms of $L^1$ and $L^2$-norms. Numerical benchmarks, including rigid body rotation and swirling deformation flows with smooth and discontinuous initial conditions, validate the scheme's accuracy, stability, and robustness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Third-order Conservative Semi-Lagrangian Discontinuous Galerkin Scheme For the Transport Equation on Curvilinear Unstructured Meshes Cai, Xiaofeng Chen, Yibing Fu, Kunkai Pan, Liujun Numerical Analysis We develop a third-order conservative semi-Lagrangian discontinuous Galerkin (SLDG) scheme for solving linear transport equations on curvilinear unstructured triangular meshes, tailored for complex geometries. To ensure third-order spatial accuracy while strictly preserving mass, we develop a high-order conservative intersection-based remapping algorithm for curvilinear unstructured meshes, which enables accurate and conservative data transfer between distinct curvilinear meshes. Incorporating this algorithm, we construct a non-splitting high-order SLDG method equipped with weighted essentially non-oscillatory and positivity-preserving limiters to effectively suppress numerical oscillations and maintain solution positivity. For the linear problem, the semi-Lagrangian update enables large time stepping, yielding an explicit and efficient implementation. Rigorous numerical analysis confirms that our scheme achieves third-order accuracy in both space and time, as validated by consistent error analysis in terms of $L^1$ and $L^2$-norms. Numerical benchmarks, including rigid body rotation and swirling deformation flows with smooth and discontinuous initial conditions, validate the scheme's accuracy, stability, and robustness. |
| title | A Third-order Conservative Semi-Lagrangian Discontinuous Galerkin Scheme For the Transport Equation on Curvilinear Unstructured Meshes |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.10100 |