Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (1): 113-141.doi: 10.1007/s42967-022-00227-9

• ORIGINAL PAPERS • 上一篇    下一篇

A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Two-Dimensional Incompressible Flow

Hao Li, Xiangxiong Zhang   

  1. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907-2067, USA
  • 收稿日期:2022-07-30 修回日期:2022-10-27 发布日期:2024-04-16
  • 通讯作者: Xiangxiong Zhang,E-mail:zhan1966@purdue.edu;Hao Li,E-mail:li2497@purdue.edu E-mail:zhan1966@purdue.edu;li2497@purdue.edu
  • 基金资助:
    The research is supported by NSF DMS-1913120.

A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Two-Dimensional Incompressible Flow

Hao Li, Xiangxiong Zhang   

  1. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907-2067, USA
  • Received:2022-07-30 Revised:2022-10-27 Published:2024-04-16
  • Contact: Xiangxiong Zhang,E-mail:zhan1966@purdue.edu;Hao Li,E-mail:li2497@purdue.edu E-mail:zhan1966@purdue.edu;li2497@purdue.edu
  • Supported by:
    The research is supported by NSF DMS-1913120.

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摘要： For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations, we show that the simple bound-preserving limiter in Li et al. (SIAM J Numer Anal 56: 3308-3345, 2018) can enforce the strict bounds of the vorticity, if the velocity field satisfies a discrete divergence free constraint. For reducing oscillations, a modified TVB limiter adapted from Cockburn and Shu (SIAM J Numer Anal 31: 607-627, 1994) is constructed without affecting the bound-preserving property. This bound-preserving finite difference method can be used for any passive convection equation with a divergence free velocity field.

关键词: Finite difference, Monotonicity, Bound-preserving, Discrete maximum principle, Passive convection, Incompressible flow, Total variation bounded limiter

Abstract: For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations, we show that the simple bound-preserving limiter in Li et al. (SIAM J Numer Anal 56: 3308-3345, 2018) can enforce the strict bounds of the vorticity, if the velocity field satisfies a discrete divergence free constraint. For reducing oscillations, a modified TVB limiter adapted from Cockburn and Shu (SIAM J Numer Anal 31: 607-627, 1994) is constructed without affecting the bound-preserving property. This bound-preserving finite difference method can be used for any passive convection equation with a divergence free velocity field.

Key words: Finite difference, Monotonicity, Bound-preserving, Discrete maximum principle, Passive convection, Incompressible flow, Total variation bounded limiter

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