A high order accurate bound-preserving compact finite difference scheme for two-dimensional incompressible flow
Numerical Analysis
2023-10-26 v1 Numerical Analysis
Abstract
For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving (SSP) temporal discretizations, we show that the simple bound-preserving limiter in [Li H., Xie S., Zhang X., SIAM J. Numer. Anal., 56 (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 B., Shu CW., SIAM J. Numer. Anal., 31 (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.
Keywords
Cite
@article{arxiv.2310.16171,
title = {A high order accurate bound-preserving compact finite difference scheme for two-dimensional incompressible flow},
author = {Hao Li and Xiangxiong Zhang},
journal= {arXiv preprint arXiv:2310.16171},
year = {2023}
}