Fractional-step High-order and Bound-preserving Method for Convection Diffusion Equations
| Autor: | Kuang, Baolin, Fu, Hongfei, Xie, Shusen |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 36 pages, 5 tables, 69 figures |
| Databáze: | arXiv |
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