CONSTRUCTION OF HIGH-ORDER ACCURACY IMPLICIT RESIDUAL SMOOTHING SCHEMES

Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (4): 407-414.

CONSTRUCTION OF HIGH-ORDER ACCURACY IMPLICIT RESIDUAL SMOOTHING SCHEMES

倪明玖, 席光, 王尚锦

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

收稿日期:1998-01-06 修回日期:1999-12-03 出版日期:2000-04-18 发布日期:2000-04-18
基金资助:
Doctoral Education Foundation of National Education Committee of China

CONSTRUCTION OF HIGH-ORDER ACCURACY IMPLICIT RESIDUAL SMOOTHING SCHEMES

Ni Mingjiu, Xi Guang, Wang Shangjin

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

Received:1998-01-06 Revised:1999-12-03 Online:2000-04-18 Published:2000-04-18
Supported by:
Doctoral Education Foundation of National Education Committee of China

摘要/Abstract

摘要： 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-order 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.

关键词: IRS scheme, four-stage Runge-Kutta technique, TVD scheme

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-order 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.

Key words: IRS scheme, four-stage Runge-Kutta technique, TVD scheme

中图分类号:

O363

倪明玖;席光;王尚锦. CONSTRUCTION OF HIGH-ORDER ACCURACY IMPLICIT RESIDUAL SMOOTHING SCHEMES[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(4): 407-414.

Ni Mingjiu;Xi Guang;Wang Shangjin . CONSTRUCTION OF HIGH-ORDER ACCURACY IMPLICIT RESIDUAL SMOOTHING SCHEMES[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(4): 407-414.

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CONSTRUCTION OF HIGH-ORDER ACCURACY IMPLICIT RESIDUAL SMOOTHING SCHEMES

CONSTRUCTION OF HIGH-ORDER ACCURACY IMPLICIT RESIDUAL SMOOTHING SCHEMES

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