计算气动声学中的高精度紧致差分格式研究  

Study on the high-accuracy compact-finite-difference schemes for computational aeroacoustics

作　　者：柳占新[1] 黄其柏[1] 胡溧[1] 袁骥轩[1] 

机构地区：[1]华中科技大学机械学院,武汉430074

出　　处：《航空动力学报》2009年第1期83-90,共8页Journal of Aerospace Power

基　　金：国家自然科学基金(50075029)

摘　　要：优化了五对角紧致差分格式.通过Fourier分析,将优化目标转化为一个求带有约束的多元非线性函数的最小值问题,利用序列二次规划(SQP)方法获得最佳系数.通过三种措施保证优化的格式具有高精度和分辨率:①直接对量化波数误差积分求其最小值;②采用绝对误差准则,使各种波长的波具有同一误差限;③优化的波数空间和精确求解区间一致.通过调整内部和边界格式的Taylor精度及误差限,保证整个格式的稳定性,并从理论上证明了优化格式具有渐进稳定性.一维和二维基准算例体现了优化格式的性能改进.The optimized pentadiagonal compact finite difference schemes were presented in this paper. Through Fourier analysis, the optimization object was converted to find the minimum of a nonlinear multi-variable function with multi-constraint. The advanced sequential quadratic programming （SQP） method was employed to find the minimum. In order to obtain high accuracy and resolution, the following strategies were applied： （1） the minimum is computed directly from integral errors of the scaled wavenumbers; （2） absolute error criterion is used for evaluating the deviation between effective and exact wavenumbers, and the waves with different wavelengths have the same error limit under this criterion; （3） the wavenumber domain for optimization is identical with the well-resolved domain. The asymptotical stability of the schemes is satisfied by adjusting the Taylor accuracy and error limits, and proved through the theoretical analysis. The increased performances of the optimized schemes are demonstrated through application to benchmark problems.

关 键 词：紧致格式 有限差分格式 序列二次规划方法 计算气动声学 渐进稳定性 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]