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

作　　者：陈小龙[1] 詹浩[1] 左英桃[1] 王晓鹏 

机构地区：[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

出　　处：《计算机仿真》2014年第5期35-38,55,共5页Computer Simulation

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。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 

分 类 号：V297[航空宇航科学技术]