三维可压缩Navier-Stokes方程的间断Galerkin有限元方法研究  

Discontinuous Galerkin method for 3-D compressible Navier-Stokes equations

作　　者：秦望龙 吕宏强[1] 伍贻兆[1] 陈正武 

机构地区：[1]南京航空航天大学航空宇航学院,江苏南京210016 [2]中国空气动力学研究与发展中心,四川绵阳621000

出　　处：《空气动力学学报》2016年第5期617-624,共8页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(11272152);航空基金(20152752033);气动噪声控制重点实验室开放课题;江苏高校优势学科建设工程资助项目

摘　　要：拓展了二维间断Galerkin(DG)有限元方法研究,将该数值方法用于三维可压缩欧拉方程和Navier-Stokes方程的求解。基于六面体网格单元,采用插值方法将物面的四边形面网格单元构造为弯曲面网格单元,更好地表述了真实物面特征;物面边界相邻体网格单元相应构造为高阶体网格单元,其余体网格单元采用八节点六面体单元,以较小的计算代价使网格满足DG方法计算需求。通过对三维带bump管道内流、圆球绕流以及旋转流线体绕流进行的数值求解,验证了边界弯曲方法的可行性及DG方法的高精度特性。此外,由于采用了隐式计算方法,仅需较少的时间步就能迭代收敛。A curved-boundary based discontinuous Galerkin （DG）method is developed for solving three-dimensional compressible Euler and N-S equations on hexahedral grids.In this method, the quadrilateral face elements are reconstructed to be curved with polynomial interpolation approach,which is better to represent the real boundary.With high-order volume elements clustering only around the boundary surface,this method is easy to implement and requires a small amount of extra computations.Numerical experiments on a variety of flow problems demonstrate that DG method can obtain high-order accurate solutions on relatively coarse grids with the presented curved boundary representation approach.It is worth noting that with an implicit time integration method,converging solutions can be achieved within several time steps.

关 键 词：间断有限元 NAVIER-STOKES方程 高精度 隐式方法 边界弯曲 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]