一种基于Picard迭代求解不可压缩Navier-Stokes方程的速度修正投影法  

Velocity-correction Schemes for Solving Incompressible Navier-Stokes Equations Based on Picard Iteration

作　　者：尹林茂 张玉龙 杨洋[1] 肖福建 蒋秉颜 YIN Linmao;ZHANG Yulong;YANG Yang;XIAO Fujian;JIANG Bingyan(Hunan Engineering Laboratory of Building Environmental Control Technology,University of South China,Hengyang,Hunan 421000,China;School of Civil Engineering,University of South China,Hengyang,Hunan 421000,China;Hunan Key Laboratory of Energy Efficiency in Prefabricated Buildings,University of South China,Hengyang,Hunan 421000,China)

机构地区：[1]南华大学建筑环境控制技术湖南省工程实验室,湖南衡阳421000 [2]南华大学土木工程学院,湖南衡阳421000 [3]南华大学装配式建筑节能技术湖南省重点实验室,湖南衡阳421000

出　　处：《计算物理》2025年第1期10-17,共8页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(11902142);湖南省自然科学基金(2019JJ50514);湖南省教育厅科学研究项目(22B0461);衡阳市科技计划项目(202002042118)资助。

摘　　要：介绍基于速度修正投影技术处理不可压缩Navier-Stokes方程的实施流程,并引入Picard线性化处理速度控制方程中的对流项,从而发展出一种基于Picard迭代的速度修正投影法。相较于传统方法,经过Picard线性化处理后的投影法可以采用更大的时间步长进行求解,提高了求解方法的稳定性,并且收敛精度也符合要求,证实了求解方法的可靠性。The implementation flow of processing incompressible Navier-Stokes equations based on velocity-correction schemes is introduced,and velocity-correction schemes based on Picard iteration is developed by introducing Picard linearization to process the convection term in the velocity governing equation.Compared with the traditional method,the projection method after Picard linearization can be solved with a larger time step,which improves the stability of the solution method,and the convergence accuracy meets the requirements,which confirms the reliability of the solution method.

关 键 词：NAVIER-STOKES方程 Picard线性化 速度修正投影法 

分 类 号：O241.82[理学—计算数学]