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

作　　者：Hao Li Xiangxiong Zhang 

机构地区：[1]Department of Mathematics,Purdue University,150 N.University Street,West Lafayette,IN,47907-2067,USA

出　　处：《Communications on Applied Mathematics and Computation》2024年第1期113-141,共29页应用数学与计算数学学报（英文）

基　　金：supported by NSF DMS-1913120.

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 

分 类 号：O17[理学—数学]