面向工程湍流的高精度数值方法  

High-order numerical methods for engineering turbulence simulation

作　　者：王圣业 邓小刚[1,2] 董义道 王东方 蔡佳鸿[1] WANG Shengye;DENG Xiaogang;DONG Yidao;WANG Dongfang;CAI Jiahong(College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China;Academy of Military Sciences,Beijing 100083,China)

机构地区：[1]国防科技大学空天科学学院,长沙410073 [2]军事科学院,北京100083

出　　处：《航空学报》2023年第15期207-229,共23页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(92252101,12002379);青年人才托举工程(2022QNRC001);国家专项工程(GJXM92579)。

摘　　要：高精度数值方法是计算流体力学理论研究中的热门和前沿,现今已逐渐走向工程实用。计算由RANS(Reynolds-Average Naiver-Stokes)方程或混合RANS/LES(Large Eddy Simulation)方程主导的湍流流动是高精度数值方法实现工程应用所面临的一个关键难题,包括数值稳定性、收敛效率、网格质量要求等方面均比单纯Navier-Stokes或Euler方程更为严峻。同时,航空航天、能源动力等领域对湍流分离、转捩、激波/湍流干扰、湍流燃烧等的准确模拟需求迫切,促使新的湍流模拟方法和模型不断涌现,对高精度数值方法的适应性、验证与确认,相关软件的兼容性等提出了挑战。基于此,对面向工程湍流的高精度数值方法发展情况进行了总结,重点包括适用于湍流方程的高精度空间离散格式和时间隐式保正格式、高精度方法框架下湍流模型的演化、工程求解面临的几何/网格问题、尺度分辨模拟时高精度格式与湍流方程的匹配及验证与确认方法,对其面临的挑战和未来发展方向进行了展望。The high-order numerical method has been a popular frontier topic in computational fluid dynamics.From the embryonic stage in the 1980s to the practical level today,efforts have been made for more than 30 years.In this process,the calculation of turbulent flows dominated by RANS(Reynolds-Average Navier Stokes)or Hybrid RANS/LES(Large Eddy Simulation)equations is a key problem in the engineering application of high-order numerical meth⁃ods.The numerical stability,convergence efficiency,mesh influence and other aspects involved in RANS are more serious than those in the pure Navier-Stokes or Euler equations.Moreover,there is an urgent need for accurate simu⁃lation of turbulence separation,transition,shock/turbulence interference,turbulent combustion,etc.in the fields of aerospace and energy and power.It promotes the continuous emergence of new turbulence models,bringing forward challenges for the adaptability of high-order methods,the compatibility of CFD software,and their verification and vali⁃dation.This paper summarizes the development of high-order methods for engineering turbulence simulations.The key points include high-order spatial schemes and temporal implicit positive-preserving schemes for turbulence equa⁃tion,evolution of turbulence models in the framework of the high-order method,geometric/mesh problems in engineer⁃ing simulations,matching of high-order schemes and turbulence models in scale-resolution simulation as well as meth⁃ods of verification and validation.Finally,the challenges and future development are prospected.

关 键 词：高精度数值方法 湍流模拟 RANS模型 混合RANS/LES 计算流体力学 

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]