## 留言板

 引用本文: 吴泽艳, 王立峰, 武哲等 . 基于简单WENO-间断Galerkin的Euler方程自适应计算[J]. 北京航空航天大学学报, 2016, 42(4): 806-814.
WU Zeyan, WANG Lifeng, WU Zheet al. Adaptive simple WENO limiter-discontinuous Galerkin method for Euler equations[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(4): 806-814. doi: 10.13700/j.bh.1001-5965.2015.0237(in Chinese)
 Citation: WU Zeyan, WANG Lifeng, WU Zheet al. Adaptive simple WENO limiter-discontinuous Galerkin method for Euler equations[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(4): 806-814. (in Chinese)

• 中图分类号: O242

## Adaptive simple WENO limiter-discontinuous Galerkin method for Euler equations

Funds: Talents Scientific Research Starting Foundation of China Three Gorges University (KJ2014B031)
• 摘要: 为了得到Euler方程的高精度、高分辨率数值解,介绍了间断Galerkin方法、三角形单元上简单WENO限制器的基本原理以及基于自适应网格加密的激波捕捉方法。将简单WENO限制器-间断Galerkin方法应用到曲边四边形单元上,通过单元边界上高斯积分点的坐标来搜索相邻单元从而得到相邻单元的单元编号,实现了基于“问题单元”的局部网格加密自适应计算。对若干典型问题进行编程计算,结果表明,简单WENO限制器可以应用到曲边四边形单元上,且可适用于局部网格加密时具有“悬挂节点”的非结构网格上的激波捕捉。

•  [1] REED W H, HILL T R.Triangular mesh methods for the neutron transport equation:LA-UR-73-479[R].Los Alamos:Scientific Laboratory,1973. [2] COCKBURN B, SHU C W.The Runge-Kutta discontinuous Galerkin method for conservation laws V:Multidimensional systems[J].Journal of Computational Physics,1998,141(2):199-224. [3] BASSI F, REBAY S.A high order accurate discontinuous finite element method for the numerical solution of the compressible Navier Stokes equations[J].Journal of Computational Physics,1997,131(2):267-279. [4] COCKBURN B, SHU C W.The local discontinuous Galerkin method for time-dependent convection diffusion systems[J].SIAM Journal on Numerical Analysis,1998,35(6):2440- 2463. [5] SHU C W. A brief survey on discontinuous Galerkin methods in computational fluid dynamics[J].力学进展,2013,43(6):541-553. SHU C W.A brief survey on discontinuous Galerkin methods in computational fluid dynamics[J].Advances in Mechanics,2013,43(6):541-553(in Chinese). [6] COCKBURN B, KARNIADAKIS G,SHU C W.The development of discontinuous Galerkin methods[M]//COCKBURN B,KARNIADAKIS G,SHU C W.Discontinuous Galerkin methods:Theory,computation and applications.New York:Springer,2000:1-50. [7] COCKBURN B, SHU C W.TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II:General framework[J].Mathematics of Computation,1989,52(186):411-435. [8] BISWAS R, DEVINE K D,FLAHERTY J.Parallel,adaptive finite element methods for conservation laws[J].Applied Numerical Mathematics,1994,14(s1-3):255-283. [9] BURBEAU A, SAGAUT P,BRUNEAU C H.A problem independent limiter for high order Runge Kutta discontinuous Galerkin methods[J].Journal of Computational Physics,2001,169(1): 111-150. [10] SURESH A, HUYNH H T.Accurate monotonicity preserving schemes with Runge Kutta time stepping[J].Journal of Computational Physics,1997,136(1):83-99. [11] RIDER W J, MARGOLIN L G.Simple modifications of monotonicity preserving limiters[J].Journal of Computational Physics,2001,174(1):473-488. [12] QIU J X, SHU C W.Runge-Kutta discontinuous Galerkin method using WENO limiters[J].SIAM Journal on Scientific Computing,2005,26(3):907-929. [13] ADJERID S, DEVINE K,FLAHERTY J,et al.A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems[J].Computer Methods in Applied Mechanics and Engineering, 2002,191(11-12):1097-1112. [14] 张来平,刘伟, 贺立新,等.一种新的间断侦测器及其在DGM中的应用[J].空气动力学学报,2011,29(4):401-406. ZHANG L P,LIU W,HE L X,et al.A shock detection method and applications in DGM for hyperbolic conservation laws on unstructured grids[J].Acta Aerodynamica Sinica,2011,29(4): 401-406(in Chinese). [15] ZHONG X, SHU C W.A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods[J].Journal of Computational Physics,2013,232(1):397-415.

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##### 出版历程
• 收稿日期:  2015-04-18
• 修回日期:  2016-07-17
• 刊出日期:  2016-04-20

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