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。
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.
作者
杨鲤铭
吴杰
董昊
杜银杰
YANG Liming;WU Jie;DONG Hao;DU Yinjie(College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)
出处
《航空学报》
EI
CAS
CSCD
北大核心
2022年第12期34-45,共12页
Acta Aeronautica et Astronautica Sinica
基金
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)。
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
discrete velocity method
fully implicit scheme
unstructured mesh
conservative correction
computational efficiency
