基于非结构网格的TTGC有限元格式的实现及在超声速流动中的应用

基于非结构网格系统,实现了时空三阶精度的TTGC有限元格式,并在三阶TTGC格式上发展了基于人工粘性的激波捕捉技术。在非结构网格下,采用这种方法对若干典型的超声速流动问题(SOD激波管、马赫数为3的前台阶流动以及马赫数为8的高超声速圆柱流动)进行了验证计算。结果表明,TTGC格式分辨率高,在粗糙网格下能够准确的模拟超声速流场中的激波、接触间断等复杂流动现象,并且能有效的控制间断附近的数值色散现象。与传统的有限体积方法相比,本文实现的TTGC有限元格式在模拟超声速流动问题方面具有格式精度高、数值耗散小等优点。

Unstructured grids based TTGC finite element scheme and its application to supersonic flows

A third order TTGC finite element method combined with shock-capturing technique is presented in the paper.The shock-capturing technique was developed on the base of artificial viscosity.Several numerical simulations of supersonic flow problems (SOD shocktube,wind tunnel with a step,hypersonic flow around a cylinder) were conducted under unstructured meshes with this method.The computation results show that the TTGC scheme has very high numerical resolution.It is capable of capturing complex flow structures in supersonic flows,such as shock wave,contact discontinuity surface,with coarse meshes.The oscillations around the shock are perfectly controlled by the artificial viscosity.Compared with the high order finite volume scheme,it has not only higher order accuracy,but also has lower numerical dissipations in simulations of supersonic flows.