任意单元间断Galerkin有限元计算方法研究

基于龙格库塔间断Galerkin(RKDG)有限元法的构造思想,通过局部坐标变换,发展了非正交单元DG有限元计算方法;借鉴非结构网格有限体积隐式计算方法,发展了适应于DG有限元方法的隐式计算方法;借鉴一维和二维(三角形单元)DG有限元限制器构造方法,提出了非正交三棱柱单元限制器方法;利用上述方法数值模拟了球头和双椭球的高超声速粘性绕流,得到了清晰的流场结构,并得到了较好的压力和热流分布,表明该方法在复杂高超声速流动的数值模拟方面具有广阔的应用前景。

Discontinuous Galerkin finite element method on 3D arbitrary elements

Based on the ideas of Runge-Kutta Discontinuous Galerkin(RKDG) finite element method(FEM) proposed by Cockburn and Shu,a three-dimensional DG-FEM is presented for arbitrary elements,including hexahedron,prism and tetrahedron.Meanwhile,the limiters for arbitrary hexahedron and prism are constructed with following the idea of RKDG limiter for 1D and 2D(triangular element only) cases.In addition,an implicit scheme is presented for viscous flows to accelerate the convergence history.The above method is validated by two hypersonic cases,e.g.hypersonic flows over sphere-nose and double-ellipsoids.The computational results show good agreements with the experimental data and results by other authors,which demonstrate the accuracy and ability of the present method for hybrid grids over complex hypersonic configurations.