用虚拟黏性法构造Navier-Stokes方程黏性项的隐式格式

doi:10.7527/S1000-6893.2014.0344

流体力学与飞行力学

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用虚拟黏性法构造Navier-Stokes方程黏性项的隐式格式

董海涛, 刘丁松

北京航空航天大学航空科学与工程学院, 北京 100191

收稿日期:2014-09-01 修回日期:2014-12-12 出版日期:2015-07-15 发布日期:2014-12-15
通讯作者: 董海涛男, 博士, 副教授, 硕士生导师。主要研究方向: 计算流体力学, 计算数学, 空天气动问题工程计算。 Tel: 010-82316577 E-mail: htdong@buaa.edu.cn E-mail:htdong@buaa.edu.cn

Implicit scheme for viscosity item of Navier-Stokes equations with pseudo-viscosity method

DONG Haitao, LIU Dingsong

School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China

Received:2014-09-01 Revised:2014-12-12 Online:2015-07-15 Published:2014-12-15

摘要/Abstract

摘要：

提出的虚拟黏性法是一种关于Navier-Stokes方程黏性项(黏性应力项和传热项)的隐式新方法。通过引入虚拟时间和虚拟黏性项,将隐式格式的构造大大简化,从而避免了大型复杂隐式差分方程组的常规求解。在虚拟时间推进过程中所需求解的方程组的系数矩阵是一个三对角矩阵,它具有计算简单且计算量小的优点。用模型方程和Navier-Stokes方程进行了数值仿真,研究各种参数对计算的影响,并在精度和效率上与显式方法进行比较,证实了算法的正确性和优势。最后分析了本文格式的适用范围。

关键词: Navier-Stokes方程, 算子分裂, 隐式格式, 虚拟黏性, 虚拟时间

Abstract:

In this paper, a new algorithm called pseudo-viscosity method is introduced. It is a new concept used to construct implicit finite difference scheme about the viscosity item of Navier-Stokes equations. The construction of implicit scheme is greatly simplified via introducing pseudo-time and pseudo-viscosity item. Thus, the common way of getting solutions of large complex implicit finite difference equations is avoided. And a tridiagonal matrix is generated for the coefficient matrix of implicit finite difference equations. It can be solved easily and has a little operation counts. Numerical simulation are made for this implicit scheme in model equation and Navier-Stokes equations. The effects of parameters in this implicit scheme are discussed with numerical simulation. What's more, the accuracy and efficiency are compared with explicit scheme to prove the validity and advantage of the implicit scheme. Finally, conditions for using this implicit scheme are analyzed in detail.

Key words: Navier-Stokes equations, operator-splitting, implicit scheme, pseudo-viscosity, pseudo-time

中图分类号:

V211.3
O35

董海涛, 刘丁松. 用虚拟黏性法构造Navier-Stokes方程黏性项的隐式格式[J]. 航空学报, 2015, 36(7): 2186-2196.

DONG Haitao, LIU Dingsong. Implicit scheme for viscosity item of Navier-Stokes equations with pseudo-viscosity method[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(7): 2186-2196.

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E-mail：hkxb@buaa.edu.cn

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用虚拟黏性法构造Navier-Stokes方程黏性项的隐式格式

Implicit scheme for viscosity item of Navier-Stokes equations with pseudo-viscosity method

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