应用于计算气动声学的优化有限紧致格式

Optimized finite compact scheme for computational aeroacoustics

对于含间断的计算气动声学问题,数值计算的格式不仅要求低耗散低色散的设计,对短波具有较高的分辨率,还要求能捕捉激波。中心紧致格式具有高精度,具有无耗散和低色散特征,但不能捕捉间断和激波;WENO格式处理间断较为成功,而耗散和色散误差相对较大.有限紧致格式可以将紧致格式与WENO格式相结合构造成混合格式,利用光滑因子之间的关系对激波区域进行自动判断,将传统的金域求解的紧致格式划分为有限的局部紧致求解,间断点上的激波捕捉铜梁自动作为局部紧致求解的边界通量,在在光滑区域具有紧致格式的高精度低耗散性质,在激波附近不产生非物理振荡。本文利用有限紧致格式思想,构造了新的适合于气动声学问题的优化有限紧致格式,将其应用于计算气动声学一维标准测试问题,对相关格式的模拟性能进行了评估,显示该格式在宽频声波传播和含有间断的声波传播模拟方面具有优势。

High resolution for short waves is required for numerical schemes for computational aeroacoustics(CAA) problems with discontinuity,therefore low dissipation and low dispersion should be satisfied and capability of shock capturing should be obtained.The central compact schemes have low dissipation and low dispersion and high order accuracy but can not capture shock,while WENO schemes can capture shock but have quite large dissipation and dispersion.The finite compact schemes have been proposed as a general methodology to construct compact-WENO hybrid schemes,which transform the global evaluation to local evaluations in finite local compact regions.The finite compact scheme imports compact scheme in smooth regions and WENO scheme in regions with discontinuities,using the relation of smooth indicators to detect the shock region,which obtains high accuracy in smooth region and impresses the unphysical oscillations around the discontinuities.Optimized finite compact schemes were constructed,with compact scheme and original WENO and optimized WENO schemes.The evaluation of the optimized finite compact scheme and related schemes for CAA benchmark problems was accomplished with several cases,resulting that the former has comparable advantages in acoustic wave propagation problems with broad band or with shock.