Fourth- and Higher-Order Semi-Lagrangian Finite Volume Methods for the Two-dimensional Advection Equation on Arbitrarily Complex Domains

Fuente: arXiv
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Main Authors: Sun, Yunxia, Liang, Kaiyi, Zhu, Yuke, Lin, Zhi, Zhang, Qinghai
Format: Preprint
Published: 2025
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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