高阶DG格式多重网格方法构造中的不同隐式策略影响研究  

Study of Different Implicit Schemes for High Order DG Multigrid Method

作　　者：李广佳[1] 郝海兵 陈智 张强[4] 

机构地区：[1]中国航天空气动力技术研究院第十一总体设计部,北京100074 [2]中国航空计算技术研究所第七研究室,西安710068 [3]中航飞机研发中心动力燃油所,西安710089 [4]西北工业大学航空学院,西安710072

出　　处：《航空工程进展》2016年第3期279-285,共7页Advances in Aeronautical Science and Engineering

基　　金：国家"973"计算项目(2014CB744803)

摘　　要：DG方法是一种非常具有潜力的高精度方法,但其在对复杂外形的数值模拟方面仍存在内存需求量大、计算量巨大等不足。为了进一步提高DG方法求解Euler方程的效率,在传统p型多重网格的基础上,结合LU-SGS和GMRES两种隐式迭代方法,研究其整体加速性能。p型多重网格方法通过对不同阶次多项式近似解进行递归迭代求解,来达到加速收敛的目的。高阶近似(p>0)使用显式龙格库塔格式,最低阶近似(p=0)使用隐式格式。对NACA0012翼型和ONERA M6机翼跨音速无粘流动进行数值模拟,结果表明:与显式TVD-RKDG时间格式相比,DG(p0)层上采用LU-SGS和GMRES的p型多重网格方法收敛速度均得到明显提高,且GMRES迭代法性能最佳,LU-SGS迭代法次之。As a kind of high order method, the DG method has great potential in the numerical simulation of complex configuration, but there are a large amount of internal memory requirement and a huge amount of com- putation. In order to further improve the efficiency of the method for solving the Euler equation, the overall ac- celeration performance is studied by combining the two implicit iterative methods of LU-SGS and GMRES. The convergence acceleration of p-multigrid method is achieved through the recursive iterative solving of different or- der polynomial approximations. In order to achieve better convergence effect, implicit scheme is implemented on the lowest-order approximation while explicit schemes are implemented on the higher-order approximations. The transonic inviscid flow around NACA0012 airfoil and ONERA M6 wing are simulated. The numerical re- suits show that, compared with the explicit TVD-RKDG method, convergence races for the p-type multigrid methods, which adopt LU-SGS or GMRES scheme on DG（po ） layer, are significantly improved, while the per- formance of GMRES iterative method is best and LU-SGS iteration is secondary.

关 键 词：间断GALERKIN方法 p型多重网格 欧拉方程 LU-SGS GMRES 

分 类 号：V211[航空宇航科学与技术—航空宇航推进理论与工程]