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
Received date: 2014-09-01
Revised date: 2014-12-12
Online published: 2014-12-15
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
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 . DOI: 10.7527/S1000-6893.2014.0344
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.
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