High-order discretization of the Reynolds stress model with anε_(β)-adaptive algorithm  

雷诺应力模型的ε_(β)自适应高阶离散化

作　　者：Xiang Fu Xiaogang Deng Shengye Wang Shichao Zheng Guangxue Wang 符翔;邓小刚;王圣业;郑世超;王光学(College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China;Chinese Academy of Military Science,Beijing 100071,China;School of Physics,Sun Yat-sen University,Guangzhou 510275,China)

机构地区：[1]College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China [2]Chinese Academy of Military Science,Beijing 100071,China [3]School of Physics,Sun Yat-sen University,Guangzhou 510275,China

出　　处：《Acta Mechanica Sinica》2022年第6期81-94,I0002,共15页力学学报（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.12002379 and 11972370);the National Key Project(Grant No.GJXM92579).

摘　　要：The Reynolds stress model(RSM)outperforms the eddy viscosity model(EVM)when simulating complex flows and has increased demand for high-order discretization.However,the complexity of the RSM equations results in poor numerical stability and weak convergence performance.One of the reasons is that the properties of Reynolds stresses are not fully considered in the design of the numerical scheme.In response to this issue,this study develops an adaptive algorithm to adjustε_(β)values(an empirical parameter in nonlinear weights)according to the magnitude and smoothness of the Reynolds stresses.This algorithm is introduced into the fifth-order weighted compact nonlinear scheme(WCNS)and is applied to the high-order discretization of the RSM.Three aeronautic test cases are simulated to investigate the performance of the algorithm.The numerical results show that,the adaptive algorithm can reduce the residual by up to 3 orders of magnitude and predict the correct weights for gradient reversals.These results confirm that the application of theε_(β)-adaptive algorithm to the high-order discretization of the RSM is beneficial both for enhancing convergence and improving resolution.雷诺应力模型(RSM)在模拟复杂流动时优于涡流黏性模型(EVM),且对高阶离散化有更高的要求.然而由于RSM方程的复杂性,其数值稳定性差,收敛性差.其中一个原因是在设计数值格式时没有充分考虑雷诺应力的特性.针对这一问题,本研究开发了一种自适应算法,根据雷诺应力的大小和平滑度调整ε_(β)值(非线性权重中的经验参数).该算法被引入到五阶加权紧致非线性格式(WCNS)中,并应用于RSM的高阶离散化.通过三个航空测试仿真实例对算法的性能进行了检验.数值结果表明,自适应算法可以将残差减少3个数量级,并预测梯度反转的正确权重.这表明将ε_(β)自适应算法应用于RSM的高阶离散化有利于提高收敛性和分辨率.

关 键 词：WCNS Reynolds stress model Adaptive algorithm RESOLUTION 

分 类 号：O31[理学—一般力学与力学基础]