Construction of High-Order Accuracy Implicit Residual Smoothing Schemes

Ni Migjiu; Xi Guang; Wang Shangjin

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Ni Migjiu, Xi Guang, Wang Shangjin. Construction of High-Order Accuracy Implicit Residual Smoothing Schemes[J]. Applied Mathematics and Mechanics, 2000, 21(4): 365-372.

Citation:

Ni Migjiu, Xi Guang, Wang Shangjin. Construction of High-Order Accuracy Implicit Residual Smoothing Schemes[J]. Applied Mathematics and Mechanics, 2000, 21(4): 365-372.

Citation:

Ni Migjiu, Xi Guang, Wang Shangjin. Construction of High-Order Accuracy Implicit Residual Smoothing Schemes[J]. Applied Mathematics and Mechanics, 2000, 21(4): 365-372.

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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

Received Date: 1998-01-06
Rev Recd Date: 1999-12-03
Publish Date: 2000-04-15

Abstract

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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References(16)

References

[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.