Fractional-step High-order and Bound-preserving Method for Convection Diffusion Equations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913498921959424 |
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| author | Kuang, Baolin Fu, Hongfei Xie, Shusen |
| author_facet | Kuang, Baolin Fu, Hongfei Xie, Shusen |
| contents | In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the one-dimensional equation into three stages, and employ appropriate temporal and spatial discrete schemes respectively. We show that our scheme is weakly monotonic and that the bound-preserving property can be achieved using the bound-preserving limiter under some mild step constraints. By employing the alternating direction implicit (ADI) method, we extend the scheme to two-dimensional problems, further reducing computational cost. We also provide various numerical experiments to verify our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional-step High-order and Bound-preserving Method for Convection Diffusion Equations Kuang, Baolin Fu, Hongfei Xie, Shusen Numerical Analysis 65M06, 65M15, 35K55 In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the one-dimensional equation into three stages, and employ appropriate temporal and spatial discrete schemes respectively. We show that our scheme is weakly monotonic and that the bound-preserving property can be achieved using the bound-preserving limiter under some mild step constraints. By employing the alternating direction implicit (ADI) method, we extend the scheme to two-dimensional problems, further reducing computational cost. We also provide various numerical experiments to verify our theoretical results. |
| title | Fractional-step High-order and Bound-preserving Method for Convection Diffusion Equations |
| topic | Numerical Analysis 65M06, 65M15, 35K55 |
| url | https://arxiv.org/abs/2409.08531 |