高精度隐式参差光滑格式的构造

倪明玖; 席光; 王尚锦

高精度隐式参差光滑格式的构造

西安交通大学能动学院(机泵中心), 西安 710049

基金项目: 国家教委博士点资金

详细信息

中图分类号: O363
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- 被引次数: 0
出版历程
- 收稿日期: 1998-01-06
- 修回日期: 1999-12-03
- 刊出日期: 2000-04-15

Construction of High-Order Accuracy Implicit Residual Smoothing Schemes

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, P R China

摘要

摘要: 参照Lax-Wendroff格式的构造方法,就双曲型方程、抛物型方程和双曲-抛物型方程,构造了一种新的IRS(implicit residual smoothing)格式。该IRS格式有二阶或三阶时间精度且大大地拓宽了解的稳定区域和CFL数。这种新的IRS格式有中心加权型和迎风偏向型两种,并用von-Neumann分析方法分析了格式的稳定范围。讨论了在透平机械中广泛应用的Dawes方法的局限性,发现该方法对稳态问题得出的解与时间步长的选取有关,对粘性问题求解时,时间步长受严格限制。最后,结合TVD(total variation diminishing)格式和四阶Runge-Kutta技术,用IRS格式和Dawes方法对二维反射激波场进行了数值模拟,数值结果支持本文的分析结论。
- Lax-Wendroff格式 /
- IRS格式 /
- 四阶Runge-Kutta技术 /
- TVD格式
Abstract: Referring to the construction way of Lax-Wendroff scheme,new IRS(Implicit Residual Smoothing) schemes have been developed for hyperbolic,parabolic and hyper-parabolic equations.These IRS schemes have 2nd-or 3rd-order time accuracy,and can extend the stability region of basic explicit time-stepping scheme greatly and thus can permit higher CFL number in the calculation of flow field.The central smoothing and upwind-bias smoothing techniques have been developed too.Based on one-dimensional linear model equation,it has been found that the scheme is unconditionally stable according to the von-Neumann analysis.The limitation of Dawes' method,which has been applied in turbomachinery widespreadly,has been discussed on solving steady flow and viscous flow.It is shown that stable solution of this method is not completely independent with the value of time step.In the end,numerical results by using IRS schemes and Dawes' method as well as TVD(total variation diminishing) scheme and four-stage Runge-Kutta technique are presented to verify the analytical conclusions.
- IRS scheme /
- four-stage Runge-Kutta technique, TVD scheme /

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参考文献(16)

[1]	傅德薰.流体力学数值模拟[M].北京:国防工业出版社,1993.
[2]	Hirsch C.Numerical Computation of Internal and External Flows,Vol.1:Fundamental of Numerical Discretization[M].Chichester:John Wiley and Sons,1988.
[3]	MacCormack R W.Current status of numerical solutions of Navier-Stokes equations[Z].AIAA Paper,85-032,1985.
[4]	Jameson A,Baker T J.Solution of the Euler equations for complex configurations[Z].AIAA Paper,83-1929,1983.
[5]	Blazek J,Kroll N,Rossow C C.A comparison of several implicit residual smoothing methods[A].In:ICFD Conference on Numerical Methods for Fluid Dynamics[C].UK:Reading,1992.
[6]	Lax P D,Wendroff B.Systems of conservation laws[J].Comm Pure Appl Math,1960,13(1):217.
[7]	Dawes W N.Application of a three-dimensional viscous compressible flow solver to a high-speed centrifugal rotor-secondary flow and loss generation[Z].IMechE,C261/87,1987.
[8]	Yee H C.Construction of explicit and implicit symmetric TVD schemes and their applications[J].J Comput Phys,1987,68(1):151～179.
[9]	Yee H C.High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows[J].J Comput Phys,1990,88(1):31～61.
[10]	Pullium T H,Chaussee D S.A diagonal form of an implicit approximate factorization algorithm[J].J Comput Phys,1981,39(2):347～363.
[11]	Chakravathy S R.Relaxation methods for unfactored implicit upwind schemes[Z].AIAA Paper,84-0165,1984.
[12]	Hathaway M D,Criss R M,Wood J R,et al.Experimental and computational investigation of the NASA low-speed centrifugal compressor flow field[J].ASME J Turbomachinery,1993,115(3):527～542.
[13]	Storer J A.Cumpsty N A.Tip leakage flow in axial compressors[J].ASME J Turbomachinery,1991,113(2):252～259.
[14]	Krain H,Hoffman W.Verification of an impeller design by laser measurements and 3D-viscous flow calculations[Z].ASME,89-GT-159,1989.
[15]	Harten A.High resolution schemes for hyperbolic conservation laws[J].J Comput Phys,1983,49(2):357～393.
[16]	Sweby P K.High resolution schemes using flux limiters for hyperbolic conservation laws[J].SIAM J Numer Anal,1984,21(5):995～1011.