高阶间断Galerkin方法求解三维欧拉方程的研究

摘要

在三维非结构网格上,对高阶间断Galerkin方法求解定常三维欧拉方程进行研究.文中使用Roe格式通量函数计算网格单元边界上的数值通量;时间方向采用显式Runge-Kutta方法推进;并引入激波探测器和斜率限制器技术,成功地抑制流场解在间断处的数值振荡.对M6机翼跨音速无粘流场进行数值模拟,结果表明:计算结果和实验值吻合较好,和同等精度的有限体积法相比,具有更低的数值耗散和更强的激波捕捉能力.%Aim.The introduction of the full paper reviews a number of papers in the open literature, points out their shortcoming and then, in its last paragraph, proposes what we believe to be an effective method of applying the DGM, which is explained in sections 1 through 5.Section 2 uses a discontinuous Galerkin finite element method to compute the compressible inviscid steady-state flow on 3-D unstructured grids and then, uses the Roe flux to discretize the nonlinear numerical flux.Sections 3 and 4 use the discontinuous detector that is based on the physical characteristics of shocks and then use the Barth-Jespersen theory to limit the slope of the flow solution, thus effectively suppressing its numerical oscillatioas.Section 5 discretizes time with the explicit fourth-order accurate RungeKutta methods.To verify the effectiveness of our method, section 6 presents a numerical simulation example of the transonic inviscid flow around an ONERA M6 wing.The simulation results, given in Figs.2 and 3, and their analysis show preliminarily that: (1) our simulation results agree well with French experimental data; (2) compared with the finite volume method of the same order, our application of DGM has smaller numerical dissipation and is more capable of capturing shocks, thus being effective for solving complex flows.