求解欧拉方程的预处理隐式无网格算法  

An implicit preconditioned gridless method for solving Euler equations at low mach numbers

作　　者：曹骋 陈红全[1] CAO Cheng;CHEN Hongquan(College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing,210016,China)

机构地区：[1]南京航空航天大学航空学院,南京210016

出　　处：《哈尔滨工业大学学报》2020年第7期161-169,共9页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金(11972189);江苏高校优势学科建设工程资助项目。

摘　　要：发展出一种用于求解欧拉方程的预处理隐式无网格算法.该算法对守恒型欧拉方程进行Weiss-Smith型矩阵预处理,并在无网格点云上离散求解.求解大体是基于传统无网格算法展开的,为此,先对矩阵谱半径、人工耗散项、远场边界条件等受预处理影响的部分进行了具体的讨论.接着,结合LU-SGS算法,通过点云重排与分割,给出了预处理隐式无网格算法的具体实施过程.典型翼型和机翼算例与文献或实验结果进行了验证比较,表明所发展的隐式算法比相应显式算法收敛更快,已从单纯模拟可压缩流动拓展到模拟几乎不可压的低马赫数流.最后,给出了翼身组合体的低马赫数绕流算例,进一步展示出算法处理实用三维气动外形的潜力.In this paper an implicit preconditioned gridless method is developed for solving Euler equations at low Mach numbers.The conservative preconditioned system is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the three dimensional Euler equations,which are discretized under the clouds of points distributed in the computational domain by using a gridless technique.The implementations of the preconditioned gridless methods are mainly based on the frame of the traditional gridless method without preconditioning,therefore the modifications corresponding to the affect terms of preconditioning such as spectral radius,artificial dissipation and farfield boundary condition are first addressed in the paper.The lower-upper symmetric Gauss-Seidel(LU-SGS)algorithm is then introduced by reordering and splitting the cloud of points to form the implicit preconditioned gridless method.The proposed method is validated by simulating flows over typical airfoils and wing.The numerical results show that the convergence of the method presented is much faster than its explicit counterpart.It is also demonstrated that the presented methods still functions for compressible transonic flow simulations and additionally,for nearly incompressible flow simulations at low Mach numbers as well.Finally,the flows over wing-body configuration at low Mach number are simulated,which intends to show the potential ability of the method presented for coping with flows over practical aerodynamic geometries.

关 键 词：无网格算法 预处理 隐式算法 三维欧拉方程 低马赫数绕流 

分 类 号：TU311[建筑科学—结构工程]