非定常流动模拟的时间离散方法

Time discretization methods in the computation of unsteady ?ow

对于不同非定常流动问题,采用合适的时间离散方法,可有效提高数值精度和计算效率.本文在总结传统时间离散方法的基础上,对近些年发展的非线性频域法、谐波平衡法、经典时间谱方法、时间谱元法、时间有限差分法等进行了系统地总结.根据离散形式的不同,将上述方法分为时域推进法、频域谐波法、时域配点法和混合方法 4大类.首先简要介绍了各类方法的数学思想以及研究进展,并重点比较了(准)周期性非定常流动计算中各方法的精度、效率以及适用范围.然后,对各种时间离散格式的特点进行总结,并就不同的非定常流动问题如何选择合适的时间离散方法给予了建议.最后,对这些新型时间离散格式在工程中的应用进行了简要介绍,并对其发展方向进行展望.

For the numerical computation of unsteady flow,the computational accuracy and efficiency would have a significant difference with different time discretization methods.This paper based on the summarize of the development situation of time discretization methods at present,briefly introduces the time discretization methods developed in recent years like the nonlinear frequency domain method,harmonic balance method,time spectral method,time spectral element method,time finite difference method and so on.Based on the difference between discrete versions,the time discretization methods can be divided into four types:time domain marching method,frequency domain harmonic method,time domain collocation method and hybrid method.This paper briefly introduces the mathematical thought and study progress of each discretization method,and selective compare the accuracy,efficiency,and scope of application of each time discretization method in the computation of unsteady flow.Then we systematically summarize the characteristic of each time discretization method and advise how to choose appropriate time discretization methods in different unsteady flow problems.Finally,briefly introduce the application of current time discretization methods in the projects and discuss the development directions of the time discretization method in the future.