【作者】 张君；

【导师】 赵宁；

【作者基本信息】 南京航空航天大学 ， 工程硕士（专业学位）， 2016， 硕士

【摘要】 本文主要研究在笛卡尔网格的基础上运用预处理方法数值模拟粘性低速流动问题,成功发展出一种基于笛卡尔网格和预处理方法的不可压低速粘性流动求解器,有效改善原求解器对于低速流动问题求解收敛慢、精度低的问题。首先,研究了自适应笛卡尔网格生成方法,并在此基础上,结合hole-map挖洞技术和基于ADT技术的“贡献单元”法,研究了混合笛卡尔网格的生成方法,在物面附近采用贴体结构网格,远场则采用笛卡尔网格,能够有效的处理多段翼型的粘性绕流问题。其次,通过对称翼型的跨声速绕流和圆柱的超音速绕流两个算例验证了本文发展的基于有限体积方法的可压缩方程求解器的可行性,并在此基础上开展了Weiss-Smith和Choi-Merkle两种预处理方法的应用研究,包括两种预处理矩阵形式的推导,HLLC数值格式的预处理修正,基于隐式LU-SGS的预处理时间推进法研究以及远场边界条件的预处理修正等。最后,使用笛卡尔网格与预处理相结合的方法计算了NACA0012对称翼型,圆柱,NLR-7301两段翼型的低速粘性绕流问题,其结果与文献结果比较基本吻合,展现了本文发展的基于笛卡尔网格的预处理方法的收敛性和有效性。同时,对两种预处理方法的收敛效果进行了比较,并对不同马赫数对收敛速度的影响进行了分析。更多还原

【Abstract】 Preconditioning method based on Cartesian grids was studied for simulating viscous low speed flows. It was successfully developed a solver for incompressibleviscous flow in low Mach number, using Cartesian grid and preconditioning method. It could effectively solve the problems of slow convergence and low precision of the former solver.First, we have studied the numerical methods based on adaptive Cartesian grids, a hybrid Cartesian grids method was studied by combining the technique of the hole-map and the method of the “donor cell” based on the ADT technique. The structured grid was adopted near the object surface while Cartesian grid was used for far field. Viscous flow problem of multi-element airfoil could be solved effectively.Then, the feasibility of the compressible equations solver of finite volume method was proved by successfully simulating the transonic flows past NACA0012 and cylinder. it was studied the application of two different preconditioning methods(Weiss-Smith and Choi-Merkle) to compressible equations solver. The pretreatment correction on HLLC data scheme was included, as well as the study of pretreatment time marching method based on implicit LU-SGS.Finally,This method which combines Cartesian grids and preconditioning method successfully simulated the viscous flows in low Mach number past NACA0012, cylinder and NLR-7301 multi-element airfoil. The numerical results agree well with the literature or experimental data, the convergence and effectiveness of the preconditioning method in this paper was proved. At the same time, the convergence effect of the two kinds of preconditioning methods were compared, and the different Mach number’s influence on the rate of convergence is analyzed.更多还原