Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.16877 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915207936212992 |
|---|---|
| author | Liang, Kaiyi Zhu, Yuke Liu, Jiyu Zhang, Qinghai |
| author_facet | Liang, Kaiyi Zhu, Yuke Liu, Jiyu Zhang, Qinghai |
| contents | We propose a fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries on a Cartesian grid. We employ the ARMS technique to give an explicit and accurate representation of moving boundaries, and introduce a cell-merging technique to overcome discontinuities caused by topological changes in cut cells and the small cell problem. We use a polynomial interpolation technique base on poised lattice generation to achieve fourth-order spatial discretization, and use a fourth-order implicit-explicit Runge-Kutta scheme for time integration. Numerical tests are performed on various moving regions, with advection velocity both matching and differing from boundary velocity, which demonstrate the fourth-order accuracy of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries Liang, Kaiyi Zhu, Yuke Liu, Jiyu Zhang, Qinghai Numerical Analysis 35G16, 35M13, 76M12, 76R99, 80M12 We propose a fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries on a Cartesian grid. We employ the ARMS technique to give an explicit and accurate representation of moving boundaries, and introduce a cell-merging technique to overcome discontinuities caused by topological changes in cut cells and the small cell problem. We use a polynomial interpolation technique base on poised lattice generation to achieve fourth-order spatial discretization, and use a fourth-order implicit-explicit Runge-Kutta scheme for time integration. Numerical tests are performed on various moving regions, with advection velocity both matching and differing from boundary velocity, which demonstrate the fourth-order accuracy of the proposed method. |
| title | A fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries |
| topic | Numerical Analysis 35G16, 35M13, 76M12, 76R99, 80M12 |
| url | https://arxiv.org/abs/2503.16877 |