半隐式龙格-库塔方法在可压缩流动中的应用
Application of Semi-Implicit Runge-Kutta Method for Compressible Flow
陈小龙 1詹浩 1左英桃 1王晓鹏2
作者信息
- 1. 西北工业大学航空学院，陕西 西安710072
- 2. 上海机电工程研究所，上海201109
- 折叠
摘要
传统求解N-S方程的时间推进方法包括显式龙格-库塔方法和隐式LU-SGS方法。显式龙格-库塔方法受稳定性限制严格，可取CFL数较小，导致计算效率较低；隐式LU-SGS方法具有良好的稳定性，可取较大的CFL数，但对残值的隐式项部分采用了简化的处理方法，导致时间精度较低。为此一种基于三步三阶显式龙格-库塔方法的半隐式龙格-库塔时间推进格式，隐式算子为采用近似雅克比通量的LU-SGS算子，在保留了三阶时间精度的基础上，提高了稳定性及收敛性。数值仿真了RAE2822超临界翼型、ONERA M6机翼、DLR-F6翼身组合体等标准算例，结果与实验数据吻合良好，并与传统的三步三阶显式龙格-库塔方法和隐式LU-SGS方法进行对比，表明改进方法具有良好的稳定性和收敛性，而且具有三阶时间精度，在求解非定常流动中具有广泛应用前景。
Abstract
Traditional time-stepping methods to solve N-S equations include the explicit Runge-kutta method and the implicit LU-SGS method. The explicit Runge-kutta method is strictly limited by the stability criterion set by the CFL condition and the constant CFL is low which leads to great loss of time. The implicit LU-SGS method is much more stable with a larger constant CFL, but the implicit part of the residual is simplified, making the time accuracy lower. In this piece of work, a semi-implicit Runge-kutta scheme based on the three stage Runge-kutta method was developed, and the implicit operator is the LU-SGS operator involving an approximation of the flux-Jacobian. The scheme can improve the stability and convergence while with third order accuracy. The calculation of the RAE 2822 supercritical airfoil, the ONERA M6 wing and the DLR-F6 wing-body combination indicates that the results equate with the experiments. Compared with the traditional explicit Runge-kutta method and implicit LU-SGS method, the improved method has better stability and convergence and the third order accuracy.
关键词
隐式龙格-库塔方法/稳定性/收敛性/三阶时间精度Key words
Implicit Runge-kutta method/Stability/Convergence/Third order accuracy引用本文复制引用
出版年
2014
NETL
NSTL
维普
万方数据