### 广义Burgers方程声爆传播模型高阶格式离散

1. 1. 中国航空工业空气动力研究院, 沈阳 110034;
2. 高速高雷诺数气动力航空科技重点实验室, 沈阳 110034
• 收稿日期:2020-10-23 修回日期:2021-01-22 出版日期:2022-01-15 发布日期:2021-01-21
• 通讯作者: 钱战森 E-mail:qianzs@avicari.com.cn
• 基金资助:
国家自然科学基金（11672280）

### High-order scheme discretization of sonic boom propagation model based on augmented Burgers equation

WANG Di1,2, QIAN Zhansen1,2, LENG Yan1,2

1. 1. AVIC Aerodynamics Research Institute, Shenyang 110034, China;
2. Aviation Key Laboratory of Science and Technology on High Speed and High Reynolds Number Aerodynamic Force Research, Shenyang 110034, China
• Received:2020-10-23 Revised:2021-01-22 Online:2022-01-15 Published:2021-01-21
• Supported by:
National Natural Science Foundation of China (11672280)

Abstract: The sonic boom prediction is one of the key technologies in the development of the new generation low-boom supersonic transport aircraft. In view of the low accuracy of the numerical scheme for the far-field propagation model of sonic boom based on the augmented Burgers equation, we study the discretization method for high-order scheme. After the physical properties of each effect term in the model is analyzed, an appropriate high-order accuracy scheme is used to discretize each term, and the classical geometric acoustic ray tracing method is adopted to calculate the propagation path of sonic boom, so as to realize the accurate prediction of ground waveform. The reliability of the high-order discrete method used in this paper is verified by the numerical simulation of the sonic boom flight test of F-5E aircraft and the standard numerical examples of the 2nd AIAA Sonic Boom Prediction Workshop on sonic boom prediction. Further results show that the high-order scheme has lower dissipation than the traditional second-order scheme, and thus can obtain higher resolution results with the same number of grids, with the grid convergence much higher than that of the traditional second-order scheme. Meanwhile, the high-order scheme also has advantages in computational efficiency. Among the effect terms of the augmented Burgers equation, the influence of the nonlinear term is more noticeable, explaining the prominence of the advantages of the adopted high-order scheme. The influence of the thermoviscous absorption term on the numerical results is small, and the improvement of calculation accuracy by using high-order scheme is not obvious. Therefore, the traditional discrete scheme can still be used in actual calculations, and the contribution of this term can even be ignored.