利用多介质PPM方法数值模拟斜激波与物质交界面的相互作用

【作者】 王晨星；

【导师】 唐维军；

【作者基本信息】 中国工程物理研究院 ， 计算数学， 2004， 硕士

【摘要】 发展适合于多介质流动的数值方法及其对复杂流动现象的模拟是近几年来的研究热点之一，比较常用的方法是利用质量分数模型方程。为防止在界面附近的压力振荡而提出了众多的数值方法。Abgrall通过接触界面两侧的压力平衡和速度一致假设导出流体体积分数等参数的演化方程，结合Euler方程组，得出了基于准守恒型控制方程组的计算模型。Shyue将该计算方法推广到基于一般刚性气体状态方程的γ模型和体积分数模型的准守恒型Euler方程组。 本文结合Abgrall／Shyue的计算模型和经典的高精度PPM方法数值模拟了多介质可压缩流动的情况。一维和二维问题的算例表明，本方法可以较好的模拟高密度比水气两相介质、带强激波的可压缩流动，对于激波和接触间断分辨率较高。文中重点数值模拟了斜激波与不同物质交界面的相互作用的演化过程，并给出了交界面上由于切向流效应产生的涡列的演化过程。更多还原

【Abstract】 It is one of the hotspots to develop the numerical methods for multi-fluids and to simulate the complex flows. The common method is using the mass fraction model equations. In order to avoid the pressure oscillation near the interface, many numerical methods are put forward. Abgrall obtained the evolution equations for volume" fraction on the assumption that the pressure retains in equilibrium and the velocity is consistent. Then he combined the evolution equations with the Euler equations, and finally got the model equations based on the quasi-conservative equations. Shyue developed the method to the quasi-conservative Eulerequations grounded on the y -model and the volume-fraction model for the multi-fluids instiffened gas equations of state.In this paper, a simple fluid-mixture type PPM algorithm for multi-component flow, which combines the fluid-mixture model of Abgrall/Shyue and the classic Piecewise-Parabolic -Method (PPM), is developed to simulate the compressible multi-fluid flows. ID and 2D numerical results show that the method can solve the multi-fluids interfacial flows correctly and be robust for high density-ratio flow and large difference of EOS at both sides of the interface. In this paper, we also present the results of numerical computations of the refraction of a plane shock wave at the different interfaces using the multi-components PPM method. We present the evolvement of the interfaces because of the baroclinic effects on the interface, especially the case of the strong shock striking at the interfaces as well.更多还原