Fourth- and Higher-Order Semi-Lagrangian Finite Volume Methods for the Two-dimensional Advection Equation on Arbitrarily Complex Domains
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908412576530432 |
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| author | Sun, Yunxia Liang, Kaiyi Zhu, Yuke Lin, Zhi Zhang, Qinghai |
| author_facet | Sun, Yunxia Liang, Kaiyi Zhu, Yuke Lin, Zhi Zhang, Qinghai |
| contents | To numerically solve the two-dimensional advection equation, we propose a family of fourth- and higher-order semi-Lagrangian finite volume (SLFV) methods that feature (1) fourth-, sixth-, and eighth-order convergence rates, (2) applicability to both regular and irregular domains with arbitrarily complex topology and geometry, (3) ease of handling both zero and nonzero source terms, and (4) the same algorithmic steps for both periodic and incoming penetration conditions. Test results confirm the analysis and demonstrate the accuracy, flexibility, robustness, and excellent conditioning of the proposed SLFV method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourth- and Higher-Order Semi-Lagrangian Finite Volume Methods for the Two-dimensional Advection Equation on Arbitrarily Complex Domains Sun, Yunxia Liang, Kaiyi Zhu, Yuke Lin, Zhi Zhang, Qinghai Numerical Analysis To numerically solve the two-dimensional advection equation, we propose a family of fourth- and higher-order semi-Lagrangian finite volume (SLFV) methods that feature (1) fourth-, sixth-, and eighth-order convergence rates, (2) applicability to both regular and irregular domains with arbitrarily complex topology and geometry, (3) ease of handling both zero and nonzero source terms, and (4) the same algorithmic steps for both periodic and incoming penetration conditions. Test results confirm the analysis and demonstrate the accuracy, flexibility, robustness, and excellent conditioning of the proposed SLFV method. |
| title | Fourth- and Higher-Order Semi-Lagrangian Finite Volume Methods for the Two-dimensional Advection Equation on Arbitrarily Complex Domains |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.15142 |