改进的间断Galerkin法在激波管中的应用  

Application of the improved discontinuous Galerkin method in shock tubes

作　　者：侯鹏 张文平[1] 明平剑[1] 那薇[1] 石非[1] 

机构地区：[1]哈尔滨工程大学动力与能源工程学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2010年第2期188-194,共7页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(90210017)

摘　　要：近几年来,新兴的间断Galerkin法在计算流体领域取得了高效成果.该文在DG方法的基础上做了2处改进:主部修正副部和间断界面上的迎风格式.改进的DG法配以迎风格式可以有效地将激波面锁定在几个网格之内,有时可达一个网格;左或右迎风格式可以有效分辨小型激波;双侧迎风格式与精确解有很好的吻合度.数值模拟结果表明,DG法具有良好的收敛性、很小的数值耗散和很好的激波捕捉能力.如果选取m个基函数,DG法可以达到m+1阶精度.构造单元界面通量函数时,不需要增加节点信息就可以提高精度,而且很容易达到高阶精度.In recent years, the discontinuous Galerkin （DG） method emerged to produce excellent results in fluid computations. However, the DG method can be improved in two areas. One area allows the main part to correct the assistant part. The improved DG method with upwind format can lock shock waves within a small number of grids, sometimes locking them into one grid. Left or right upwind format can distinguish mini type shock waves, and the dual lateral upwind format can provide a better fit, and thus a more precise solution. Results of numerical simula- tions showed that the DG method has many helpful characteristics, such as good convergence, small numerical dis- sipation and good shock wave capturing ability. If you select an m -basis function, the DG method can achieve m ＋ 1 order accuracy. When calculating the interface flux function we need no additional nodal information and accura- cy is improved. In addition, it is very easy to achieve high-order accuracy.

关 键 词：间断Galerkin法 激波 分辨率 迎风格式 

分 类 号：O35[理学—流体力学]