Fractional-step High-order and Bound-preserving Method for Convection Diffusion Equations
<|reference_start|>Fractional-step High-order and Bound-preserving Method for Convection Diffusion Equations: 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.<|reference_end|>
@article{kuang2024fractional-step,
    title={Fractional-step High-order and Bound-preserving Method for Convection
  Diffusion Equations},
    author={Baolin Kuang, Hongfei Fu and Shusen Xie},
    journal={arXiv preprint arXiv:2409.08531},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.08531},
    primaryClass={math.NA cs.NA}
}