基于p-多重网格的间断Galerkin方法研究  

Novelly Combining Discontinuous Galerkin Method with p-Multigrid Technology

作　　者：郭永恒[1] 杨永[1] 段治健[1] 

机构地区：[1]西北工业大学翼型叶栅空气动力学国防科技重点实验室,陕西西安710072

出　　处：《西北工业大学学报》2010年第2期187-191,共5页Journal of Northwestern Polytechnical University

摘　　要：文章采用规范正交基作为测试函数,基于p-多重网格的思想,建立了间断Galerkin方法的二重网格格式,并以此求解了Euler方程,数值模拟了绕NACA0012和RAE2822翼型的跨音速流场。其中,在网格交界处采用Roe的迎风型数值通量。沿时间方向,高阶格式和低阶格式上分别采用Runge-Kutta方法和LUSGS方法推进。通过对残值收敛曲线的比较,认为文中的p-多重网格算法取得了非常优良的加速收敛效果。Aim.In our opinion,Ref.1′s discontinuous Galerkin method is good in calculation precision but its slow convergence puts severe limits on its application to engineering problems.Hence we propose our novel solver for accelerating convergence.This solver can be used to compute transonic flows such as the flows respectively over the airfoils NACA0012 and RAE2822.Section 1 of the full paper briefs the high-order p-multigrid and points out its peculiarities when used in our solver;these peculiarities are eqs.（7） and（8）.Section 2 merely briefs the low-order p-multigrid.Section 4 briefs the constructions respectively of restrictive operator and topological operator and points out their peculiarities when used in our solver;these peculiarities are eqs.（20）,（21） and（22）.Section 5 explains how to use our novel solver;its core consists of：（1） the numerical flux of the Euler equations is calculated by using the Roe scheme;（2） along the direction of time,the explicit Runge-Kutta scheme and the implicit LUSGS scheme are applied respectively to the high-order p-multigrid and the low-order p-multigrid.The results computed for NACA0012 airfoil are presented in Figs.1 through 4 and those for RAE2822 airfoil are presented in Figs.5 through 8.These results show preliminarily that,compared with the solver in Ref.1,our novel solver delivers a convergence rate that is approximately one order higher.

关 键 词：规范正交基 p-多重网格 间断Galerkin 

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]