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arXiv · 2310.16170

A high order accurate bound-preserving compact finite difference scheme for scalar convection diffusion equations

Hao Li·Shusen Xie·Xiangxiong Zhang
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Abstract

We show that the classical fourth order accurate compact finite difference scheme with high order strong stability preserving time discretizations for convection diffusion problems satisfies a weak monotonicity property, which implies that a simple limiter can enforce the bound-preserving property without losing conservation and high order accuracy. Higher order accurate compact finite difference schemes satisfying the weak monotonicity will also be discussed.

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Hao Li, Shusen Xie, Xiangxiong Zhang. 2023-10-24. A high order accurate bound-preserving compact finite difference scheme for scalar convection diffusion equations. https://doi.org/10.13039/100000001

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