增强优化格式在声散射问题中的应用

Application of enhanced optimized difference schemes in acoustic scattering

优化差分格式一般用于气动声学和湍流等多尺度问题的数值模拟,这类格式为了获得更精确的数值结果通常牺牲了收敛精度阶数。文献[1]中构造了一种七点模板上最高阶精度格式与优化格式的加权组合格式,该格式达到了最优阶收敛精度,并获得了更好的谱分辨率性质。由于该格式比普通优化格式具有更好的谱分辨率性质,这里称其为增强优化格式。本文将讨论基于不同优化格式构造的增强优化格式,通过线性传播方程的数值测试选取表现相对较好的增强优化格式,然后针对声波散射问题进行数值模拟与分析。结果表明,该格式计算结果与六阶中心紧致格式相近,但所需计算时间更短;此外,增强优化格式为显式格式,因此相比紧致格式更容易处理边界条件以及更容易进行并行计算。

The optimized difference schemes are usually employed for computational aeroacoustics(CAA)problems and the numerical simulations of multiscale turbulence problems.However,the good resolution on short waves is obtained at the cost of a degradation of the accuracy order.In paper[1],a hybridization of the optimized scheme and the highest order scheme is proposed to improve the accuracy order and the spectral resolution,which is a weighted convex combination of the two schemes.Because of its better resolution property,this scheme is called as the enhanced optimized scheme here.In this paper,some enhanced optimized schemes are constructed based on different optimized schemes,and then one of them is chosen according to the computation results for linear advection problems.At last,the sound wave scattering problem is used to validate the ability of the chosen enhanced optimized scheme.This scheme obtains results close to those of the sixth order central compact scheme,but with smaller time consumption.Furthermore,compared with compact schemes,it is easier to deal with the boundary condition and to implement parallel computing for this scheme.