P-Multigrid Solution of Discontinuous Galerkin Discretizations of Euler Equations on Unstructured Meshs
The purpose of this paper is to simulate the transonic flow using the discontinuous Galerkin method associating with p -multigrid scheme. Usually, explicit temporal discretization such as multi-stage TVD Runge-Kutta schemes (TVD-RKDG) is used to advance the solution in time. However, for large-scale simulations and especially for high-order solutions, the rate of convergence slows down dramatically which is strictly restricted by CFL number, resulting in inefficient solution techniques to steady state solutions. To speed up convergence, a fast, low storage p -multigrid method is introduced in this article. Unlike the traditional p -multigrid methods where the same time integration scheme is used on all approximation levels, we use an explicit multi-stage Runge-Kutta scheme as the iterative smoother on the higher level approximations and a matrix-free implicit LU-SGS implicit method as the iterative smoother on the lowest level approximation. Numerical simulation for both 2D and 3D Euler Equations are presented to demonstrate the efficiency of the p multigrid method. The results show that p-multigrid method could accelerate the convergence speed nearly one order of magnitude and maintain the original accuracy, compared with explicit form-stage TVD Runge-Kutta method.
discontinuous Galerkin methods (DGM) p-multigrid LU-SGS Euler equation
Hao Haibing Yang Yong
National Key Laboratory of Science and Technology on Aerodynamic Design and Research,Northwestern Polytechnical University, Xian 710072, China
国际会议
2010 Asia-Pacific International Symposium on Aerospace Technology(2010 亚太航空航天技术研讨会 APISAT 2010)
西安
英文
301-304
2010-09-01（万方平台首次上网日期，不代表论文的发表时间）