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.
Hao Li, Xiangxiong Zhang
. A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Two-Dimensional Incompressible Flow[J]. Communications on Applied Mathematics and Computation, 2024
, 6(1)
: 113
-141
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DOI: 10.1007/s42967-022-00227-9
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