Title: Implicit High-Order Gas Kinetic Scheme for Turbulence Simulation Show Chinese title

Title: 适用于湍流模拟的隐式高阶气体动理学格式

Abstract: In recent years, coupled with traditional turbulence models, the second-order gas-kinetic scheme (GKS) has been used in the turbulent flow simulations. At the same time, high-order GKS has been developed, such as the two-stage fourth-order scheme (S2O4) GKS, and used for laminar flow calculations. In this paper, targeting on the high-Reynolds number engineering turbulent flows, an implicit high-order GKS with Lower-Upper Symmetric Gauss-Seidel (LU-SGS) technique is developed under the S2O4 framework. Based on Vreman-type LES model and $k - \omega$ SST model, a turbulent relaxation time is obtained and used for an enlarged particle collision time in the implicit high-order GKS for the high-Reynolds number turbulent flows. Numerical experiments include incompressible decaying homogeneous isotropic turbulence, incompressible high-Reynolds number flat plate turbulent flow, incompressible turbulence around NACA0012 airfoil, transonic turbulence around RAE2822 airfoil, and transonic high-Reynolds number ARA M100 wing-body turbulence. Comparisons among the numerical solutions from current implicit high-order GKS, the explicit high-order GKS, the implicit second-order GKS, and experimental measurements have been conducted. Through these examples, it is concluded that the high-order GKS has high accuracy in space and time, especially for smooth flows, obtaining more accurate turbulent flow fields on coarse grids compared with second-order GKS. In addition, significant acceleration on computational efficiency, as well as super robustness in simulating complex flows are confirmed for current implicit high-order GKS. This study also indicates that turbulence modeling plays a dominant role in the capturing physical solution, such as in the transonic three-dimensional complex RANS simulation, in comparison with numerical discretization errors. Show Chinese abstract

Abstract: 近年来，结合传统湍流模型，二阶气体动理学格式（GKS）已被用于湍流模拟。 同时，高阶GKS也被开发出来，如两阶段四阶格式（S2O4）GKS，并用于层流流动计算。 在本文中，针对高雷诺数工程湍流，在S2O4框架下开发了一种带有低-上对称高斯-赛德尔（LU-SGS）技术的隐式高阶GKS。 基于Vreman型LES模型和$k - \omega$SST模型，获得了一个湍流松弛时间，并用于高雷诺数湍流隐式高阶GKS中的扩大粒子碰撞时间。 数值实验包括不可压缩衰减各向同性湍流、不可压缩高雷诺数平板湍流、不可压缩NACA0012翼型周围的湍流、RAE2822翼型周围的跨音速湍流以及跨音速高雷诺数ARA M100机翼-机身湍流。 已经进行了当前隐式高阶GKS的数值解、显式高阶GKS、隐式二阶GKS与实验测量结果之间的比较。 通过这些例子得出结论，高阶GKS在空间和时间上具有高精度，特别是在光滑流动中，与二阶GKS相比，在粗网格上可以获得更准确的湍流场。 此外，当前隐式高阶GKS在计算效率方面有显著提升，并且在模拟复杂流动时表现出超强的鲁棒性。 本研究还表明，湍流建模在捕捉物理解中起着主导作用，例如在跨音速三维复杂RANS模拟中，与数值离散误差相比。