新型高分辨率格式及其在CFD的应用

A New High Resolution Scheme and Its Application in CFD

利用小波奇异分析构造了一种新型的高分辨率高效计算格式,借助小波奇异分析所找到的流场中奇异点区域和光滑区域,合理选择高分辨率、高精度WENO格式和高精度中心差分格式进行流场的离散求解;利用该格式对超声速二维前台阶流动问题、跨声速RAE2822典型翼型的二维外流场、跨声速VKI-LS59涡轮叶栅的二维流场以及NASARotor37跨声速压气机转子和NASARotor67跨声速风扇转子的三维流场进行数值模拟,计算结果表明,采用这种新型格式可以用于内外流复杂流场计算。数值计算还发现,在采用相同网格的情况下,本文格式不仅具有通常WENO格式高分辨率的特点,而且计算效率较WENO格式高出3～5倍。

In this paper, a new high resolution scheme based on wavelet singularity analysis is proposed. Wavelet transform is used to analyze the flow fields and the wavelet coefficients are used to control the numerical method. In order to verify the effectiveness of the new method, five typical examples are calculated： 2D supersonic flow over a forward-facing step; 2D transonic flow over the RAE 2822 airfoil; 2D transonic flow through the VKI-LS59 turbine cascade; 3D transonic flow in axial compressor rotor, NASA Rotor 37 and 3D transonic flow in axial fan rotor, NASA Rotor 67. The numerical results show that this new high resolution scheme can be used in complex internal and external flow fields, and the new method can better capture the discontinuity （such as rarefaction wave, contact discontinuity and shock wave） in the flow fields. Compared with TVD schemes （Total Variations Diminishing schemes）, ENO schemes （Essentially Non-Oscillatory shock capturing schemes）, the new method is more efficient because TVD and ENO are only used for the grids with singularity. It is also shown that with the new method, the same resolution for the shock wave can be achieved under the same computational grids but with much reduced computation time, about one fifth of that by TVD/ENO schemes.