首页|A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Two-Dimensional Incompressible Flow
A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Two-Dimensional Incompressible Flow
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For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discre-tizations,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.
Finite differenceMonotonicityBound-preservingDiscrete maximum principlePassive convectionIncompressible flowTotal variation bounded limiter
Hao Li、Xiangxiong Zhang
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Department of Mathematics,Purdue University,150 N.University Street,West Lafayette,IN 47907-2067,USA
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