基于速度空间非结构网格和守恒修正的改进离散速度方法

杨鲤铭; 吴杰; 董昊; 杜银杰

doi:10.7527/S1000-6893.2022.27033

航空学报 >

2022 , Vol. 43 >Issue 12: 627033 - 627033

DOI: https://doi.org/10.7527/S1000-6893.2022.27033

临近空间高速飞行器数值模拟技术专栏

基于速度空间非结构网格和守恒修正的改进离散速度方法

杨鲤铭 ,
吴杰 ,
董昊 ,
杜银杰

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南京航空航天大学航空学院, 南京 210016

收稿日期: 2022-02-14

修回日期: 2022-03-17

网络出版日期: 2022-03-30

基金资助

江苏省自然科学基金（BK20210273）；江苏高校优势学科建设工程资助项目（PAPD）

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Improved discrete velocity method based on unstructured mesh in velocity space and conservative correction

YANG Liming ,
WU Jie ,
DONG Hao ,
DU Yinjie

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College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received date: 2022-02-14

Revised date: 2022-03-17

Online published: 2022-03-30

Supported by

Natural Science Foundation of Jiangsu Province (BK20210273); Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)

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摘要

传统离散速度方法在求解跨流域流动问题时，通常只求解动理学模型方程，即Boltzmann-BGK方程。与传统方法不同，改进离散速度方法同步求解了动理学模型方程和相应的宏观伴随方程。通过这种方式，可以将分子碰撞影响考虑到宏观伴随方程的通量计算中，同时宏观方程预估得到的结果可以用于预估平衡态，从而实现Boltzmann-BGK方程的全隐式离散。这两点改进可以有效克服传统方法在连续和近连续流区域计算效率低、计算精度差的缺陷。为了进一步减少速度空间的网格量和避免数值求积时的Runge现象，采用了非结构网格结合矩形律来离散速度空间并引进守恒修正来强制满足相容性条件。算例测试表明，采用速度空间非结构网格和守恒修正可以有效减少改进离散速度方法的计算量和内存花销。

关键词： 离散速度方法; 全隐式格式; 非结构网格; 守恒修正; 计算效率

本文引用格式

杨鲤铭 , 吴杰 , 董昊 , 杜银杰 . 基于速度空间非结构网格和守恒修正的改进离散速度方法[J]. 航空学报, 2022 , 43(12) : 627033 -627033 . DOI: 10.7527/S1000-6893.2022.27033

Abstract

Conventional Discrete Velocity Method (DVM) only resolves the kinetic equation (i.e., Boltzmann-BGK equation) in each time step for fluid flow problem simulation in all flow regimes. Different from the conventional method, the Improved Discrete Velocity Method (IDVM) solves both the kinetic equation and the corresponding macroscopic governing equations so that the collisional effect at the cell interface can be involved in the calculation of numerical flux and the fully implicit discretization of the kinetic equation realized by the predicted results of macroscopic governing equations. These two improvements can effectively overcome the defects of low efficiency and poor accuracy of the conventional DVM in the continuum flow regime. To further reduce the number of discrete points in the velocity space and avoid the Runge phenomenon for numerical quadrature, the unstructured mesh combined with the rectangle rule is utilized to discretize the velocity space, and the conservative correction introduced to enforce the compatibility condition. Numerical results show that these strategies can significantly reduce the computational cost and memory consumption of the present method.

Key words： discrete velocity method; fully implicit scheme; unstructured mesh; conservative correction; computational efficiency

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