群速度控制格式及二维Riemann解

Group velocity control scheme and two-dimensional riemann solver

强激波和强接触间断的数值模拟一直是计算流体力学里一个富有挑战性的课题,它们是很多实际流动的基础。三阶迎风紧致格式是一种具有较高分辨率的高精度方法,但是在计算激波时仍有数值振荡产生。本文根据数值解的群速度特性,在三阶迎风紧致格式的基础上提出了一种群速度控制格式,使得能够正确模拟含有强激波和强接触间断的复杂流动。在此基础上构造了求解包含大压力比和密度比的二维界面问题的数值方法。计算结果表明,方法对激波和接触间断的分辨效果是令人满意的。

It is a challenging work to simulate flows with strong shock waves and contact discontinuities in the field of computational fluid dynamics, which are the basic elements of many practical flows. The 3rd order upwind compact scheme is of the character of high precision and high resolution, but numerical oscillation occurs when it is used to simulate shock waves. According to the characters of group velocity, a group velocity control (GVC) scheme was constructed based on the 3rd order upwind compact scheme, which can simulate the complex flows with strong shock waves and contact discontinuities correctly. Based on the GVC scheme, a numerical solver was constructed to simulate two-dimensional interface problems of high pressure ratio and high density ratio. Numerical results show that it is an effective method to identify shock waves and contact discontinuities.