基于人工粘性的间断Galerkin有限元方法  

Discontinuous Galerkin method based on artificial viscosity

作　　者：于剑[1] 阎超[1] 

机构地区：[1]北京航空航天大学航空科学与工程学院,北京100191

出　　处：《空气动力学学报》2013年第3期371-375,共5页Acta Aerodynamica Sinica

基　　金：国家重点基础研究发展计划(2009CB724104)

摘　　要：发展了一种基于人工粘性的间断Galerkin有限元方法,作出改进以增强适应性,并向非均匀网格推广。选取了典型算例对方法进行验证。一维激波管算例表明,改进的方法在保持计算结果高分辨率的同时,能够更好地抑制非物理振荡。分析得知,当人工粘性方法用于二阶DG格式时,所得计算结果的数值耗散较大,而当格式精度大于二阶时,采用人工粘性方法所得的结果的分辨率较高。通过计算圆柱高超声速粘性绕流,将三阶DG格式与三阶MUSCL格式和五阶WENO格式的结果进行对比,结果表明,该人工粘性方法对于高超声速流动计算也具有一定的优势。The discontinuous Galerkin finite-element method based on artificial viscosity is developed. The method is modified for better adaptability and extended to curvilinear meshes. Typical test cases are sim- ulated to evaluate the method. The calculation results of a one-dimensional shock tube problem show that the modified method is able to suppress spurious oscillations well while preserving high resolution. Furthermore, with second order scheme, the artificial viscosity method is rather diffusive, and with the order of the scheme further increased, the resolution of the results is greatly improved. Also in a hypersonic cylinder flow, the artificial viscosity method shows advantage over the third-order MUSCL scheme and the fifth-order WENO scheme.

关 键 词：间断Galerkin有限元 人工粘性 激波捕捉 高超声速 气动热 

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]