三维复杂流动的间断有限元方法模拟

本文基于三维可压缩Euler方程,采用基于Runge-Kutta时间离散的间断有限元方法(RKDG方法),对三维前台阶、三维Riemann问题和球Riemann等问题进行了模拟。结果表明,本文的RKDG方法能够在很少的网格内清晰地捕捉到三维复杂流场中的激波和接触间断;同时,将球Riemann问题中z=0.4平面压强沿到对称轴距离的分布与文献中的近似精确解相比,吻合较好,这也验证了本文的RKDG方法不仅能够进行三维复杂流场的定性描述,也能够应用于三维复杂流场的定量计算。

Numerical simulation of three dimensional complex flows with RKDG method

The 3rd order accurate Runge-Kutta discontinuous Galerkin (RKDG) method is developed to simulate three dimensional complex flows,such as three dimensional forward step problem,three dimensional Riemann problem and ball Riemann problem.Numerical results show that RKDG method can capture shocks and contact discontinuities in few grid points successfully.Furthermore,the pressure distribution of z=0.4 plane in ball Riemann problem agrees well with the result in the reference by refined grids.This suggested that the RKDG method developed in this paper is not only able to qualitatively describe three-dimensional complex flows,but also can be used in quantitative three-dimensional complex flow field calculations.