摘要
数值稳定性问题一直是困扰格子玻尔兹曼方法在高雷诺数高马赫数流动中广泛应用的瓶颈。在格子玻尔兹曼方法领域改良碰撞模型的数值稳定性和精度一直是近30年来的研究难点和热点。正则化碰撞模型作为众多碰撞模型的一个重要分支,近几年来取得了重要理论进展,目前已在高雷诺数湍流模拟、高马赫数可压缩流动以及气动声学领域得到了广泛应用。本文系统地回顾了正则化碰撞模型的发展历史,并建立了一个系统的理论框架阐述不同正则化碰撞模型之间的理论联系。同时,揭示了正则化多松弛碰撞模型的理论本质,就是在与坐标无关且自相似的矩空间中将离散格子模型表达不了的高阶动理学矩进行快速松弛,以避免虚假模态对水动力学方程的影响。
Numerical stability has always been the bottleneck that plagues the wide application of lattice Boltzmann methods in the scenario of high Reynolds number and high Mach number flows.It has been a research hotspot and difficulty in the past three decades to improve the numerical stability and accuracy of the collision models for lattice Boltzmann methods.As an important branch of many collision models,the regularized collision model has made massive theoretical progress in recent years,and has been widely applied in the fields of high Reynolds number turbulent flow,high Mach number compressible flow and aeroacoustics flow.The present study systematically reviews the development history of regularized collision models,and establishes a systematic theoretical framework to illustrate the underlying theoretical connection among different regularized collision models.Meanwhile,the present work reveals the theoretical essence of the regularized multi-relaxation collision model,which is to rapidly relax the higher-order kinetic moments that cannot be expressed by the discrete lattice model in a coordinate-independent and self-similar moment space,so as to avoid the spurious modes affecting the hydrodynamic equations.
作者
李旭晖
单肖文
段文洋
LI Xuhui;SHAN Xiaowen;DUAN Wenyang(College of Shipbuilding Engineering,Harbin Engineering University,Harbin 150001,China;Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen 518055,China)
出处
《空气动力学学报》
CSCD
北大核心
2022年第3期46-64,I0001,共20页
Acta Aerodynamica Sinica
基金
哈尔滨工程大学中央高校基本业务费(3072021CFJ0101)
黑龙江省自然科学基金联合引导项目(LH2021A007)。
