On General Form of Navier-Stokes Equations and Implicit Factored Scheme

Wang Bao-guo

Volume 9 Issue 2

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1988 > 9(2): 165-172

Wang Bao-guo. On General Form of Navier-Stokes Equations and Implicit Factored Scheme[J]. Applied Mathematics and Mechanics, 1988, 9(2): 165-172.

Citation:

Wang Bao-guo. On General Form of Navier-Stokes Equations and Implicit Factored Scheme[J]. Applied Mathematics and Mechanics, 1988, 9(2): 165-172.

Citation:

Wang Bao-guo. On General Form of Navier-Stokes Equations and Implicit Factored Scheme[J]. Applied Mathematics and Mechanics, 1988, 9(2): 165-172.

PDF( 474 KB)

On General Form of Navier-Stokes Equations and Implicit Factored Scheme

Wang Bao-guo

Institute of Engineering Thermophysics, Academia Sinica, Beijing

Received Date: 1986-08-01
Publish Date: 1988-02-15

Abstract

Abstract

A general weak conservative form of Navier-Stokes equations expressed with respect to non-orthogonal Curvilinear coordinates and with primitive variables was obtained by using tensor analysis technique, where the contravariant and covariant velocity components were employed. Compared with the current coordinate transformation method, the established equations are concise and forthright, and they are more convenient to be used for solving problems in body-fitted curvilinear coordinate system. An implicit factored scheme for solving the equations is presented with detailed discussions in this paper. For n-dimensional flow the algorithm requires n-steps and for each step only a block tridiagonal matrix equation needs to be solved. It avoids inverting the matrix for large systems of equations and enhances the speed of arithmetic. In this study, the Beam-Warming's implicit factored schceme is extended and developed in non-orthogonal curvilinear coordinate system.

FullText(HTML)

References(12)

References

[1]	吴仲华,《叶轮机械三元流动讲义》,中国科技大学(1975).
[2]	Thompson, J.F., Grid generation techniques in computational fluid dynamics, J. AIAA, 22 (1984), 1505-1523.
[3]	王保国,跨声速流函数方程强隐式解及确定密度场的新方案,计算物理,2,41985),474-481.
[4]	钱伟长,粘性流体力学的变分原理和广义变分原理,应用数学和力学,5, 3 (1984), 305-322.
[5]	Beam, R.M. and R.F. Warming, An implicit factored scheme for the compressible Navier-Stokes equations J. AIAA, 16 (1978), 393-402.
[6]	MacCormack, R.W., A numerical method for solving the equations of compressible viscous flow, AIAA paper 81-0110 (1981).
[7]	Steger, J.L., Implicit finite-difference simulation of flow about arbitrary two-dimensional geometries, J. AIAA, 16 (1978), 679-686.
[8]	王保国,使用非正交曲线坐标和作正交速度分量的含分流叶栅或串列叶栅的s₁流面正问题流场矩阵解,研究生学位论文,中国科学院工程热物理研究所(1981).
[9]	Chapman, S. and J.G. Cowling, The Mathematical Theory of Non-Uniform Gases, Cambridge (1970).
[10]	卞荫贵,《边界层理论》(上、下册),中国科技大学(1979).
[11]	H.A.基利契夫斯基著,郭乾荣译,《张量计算初步及其在力学上的应用》,高等教育出版社(1962).
[12]	张涵信,差分计算中激波上、下游解出现波动的探讨,空气动力学学报,1 (1984), 12-19.

Relative Articles

[1]	GUO Yong, XIE Jian-hua. N-S Bifurcation of an Oscillator With Dry Friction in 1∶4 Strong Resonance[J]. Applied Mathematics and Mechanics, 2013, 34(1): 18-26. doi: 10.3879/j.issn.1000-0887.2013.01.003
[2]	YANG Ming, SHI Pei-hu. Bifurcation of Non-Negative Solutions for an Elliptic System[J]. Applied Mathematics and Mechanics, 2008, 29(2): 228-234.
[3]	SHI Wei-hui, WANG Yue-peng. Impact of Singularity of Navier-Sokes Equation Upon the Atmospheric Motion Equations[J]. Applied Mathematics and Mechanics, 2007, 28(5): 614-618.
[4]	SHI Wei-hui, SHEN Chun, WANG Yue-peng. Analytical Solution of the Basic Equations Set of Atmospheric Motion[J]. Applied Mathematics and Mechanics, 2007, 28(3): 349-358.
[5]	YUAN Yu-bo, PU Dong-mei, LI Shu-min. Bifurcations of Travelling Wave Solutions in Variant Boussinesq Equations[J]. Applied Mathematics and Mechanics, 2006, 27(6): 716-726.
[6]	XU Gui-qiong, LI Zhi-bin. Explicit Solutions to the Coupled KdV Equations with Variable Coefficients[J]. Applied Mathematics and Mechanics, 2005, 26(1): 92-98.
[7]	WEN Gong-bi, CHEN Zuo-bin. Unsteady/Steady Numerical Simulation of Three-Dimensional Incompressible Navier-Stokes Equations on Artificial Compressibility[J]. Applied Mathematics and Mechanics, 2004, 25(1): 53-66.
[8]	SHI Wei-hui, SHEN Zhen. Formal Solutions and Projective Limit of P. D. E[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1133-1140.
[9]	LI Da-ming, ZHANG Hong-ping, GAO Yong-xiang. Series Perturbations Approximate Solutions to N-S Equations and Modification to Asymptotic Expansion Matched Method[J]. Applied Mathematics and Mechanics, 2002, 23(8): 855-863.
[10]	HUANG Wen-hua, SHEN Zu-he. On the Existence of Solutions of Boundary Value Problems of Duffing Type Systems[J]. Applied Mathematics and Mechanics, 2000, 21(8): 875-880.
[11]	Fang Jinxuan, Song Guian. A Note on Probabilistic Contractor Couple and Solutions for a System of Nonlinear Equations in N.A.Menger PN-Spaces[J]. Applied Mathematics and Mechanics, 2000, 21(7): 759-765.
[12]	Yin Yihui, Chen Gang, Chen Yuze. A Solving Method for a System of Partial Differential Equations With an Application to the Bending Problem of a Thick Plate[J]. Applied Mathematics and Mechanics, 1999, 20(11): 1168-1174.
[13]	Ding Xieping, Wang Fan. Solutions for a System of Nonlinear Random Integral and Differential Equations under Weak Topology[J]. Applied Mathematics and Mechanics, 1997, 18(8): 669-684.
[14]	Cat Rizeng, Xu Zhenyuan. Approximate Inertial Manifolds for the System of the J-J Equations[J]. Applied Mathematics and Mechanics, 1996, 17(4): 327-334.
[15]	Hou Yanren. Fourier Nonlinear Galerkin Approximation for the Two Dimensional Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1996, 17(9): 829-836.
[16]	Liu Xiao-xiang. The Differential Solution to the Flying Locus Equation of the Shot and Its Application[J]. Applied Mathematics and Mechanics, 1994, 15(11): 1031-1035.
[17]	Pan Zhong-xiong, Wang Yi-fei. Numerical Method for the System of Reaction-Diffusion Equations with a Small Parameter[J]. Applied Mathematics and Mechanics, 1991, 12(8): 761-767.
[18]	Lin Wu-zhong. Singular Perturbation of Linear Algebraic Equations with Application to Stiff Equations[J]. Applied Mathematics and Mechanics, 1987, 8(6): 513-522.
[19]	Li Qing-xi. Convergence of the Approximate Solution for the Elliptic Boundary Value Problem[J]. Applied Mathematics and Mechanics, 1987, 8(5): 405-411.
[20]	Liang Zhong-chao, Chen Shao-zhu. Proper Solutions and Limit Boundary Value Problems of Nonlinear Second-Order Systems of Differential Equations[J]. Applied Mathematics and Mechanics, 1985, 6(11): 1027-1034.