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Mie-Grneisen状态方程可压缩多流体流动的PPM方法
引用本文:郑建国,马东军,孙德军,尹协远.Mie-Grneisen状态方程可压缩多流体流动的PPM方法[J].爆炸与冲击,2006,26(2):156-162.
作者姓名:郑建国  马东军  孙德军  尹协远
作者单位:1.中国科学技术大学工程科学学院,安徽 合肥 230027
基金项目:国家自然科学基金委员会与中国工程物理研究院联合基金项目(10376035),中国博士后科学基金项目(2004036160)
摘    要:采用流体体积分数的混合型多流体数值模型,将piecewise parabolic method (PPM)方法应用于可压缩多流体流动的数值模拟,拓展了以前提出的模型和数值方法,使它能够处理一般的Mie-Grneisen状态方程。采用双波近似和两层迭代算法求解一般状态方程的Riemann问题;并根据多流体接触界面无振荡原则设计高精度计算格式,对典型的纯界面平移问题可以从理论上证明本算法在接触间断附近压力和速度没有振荡,而且数值模拟结果表明界面数值耗散也被控制在2~3个网格之内。模拟了多种复杂的可压缩多流体流动,算例结果表明本文方法可以有效地处理接触间断、激波等物理问题,且具有耗散小精度高的特点。

关 键 词:爆炸力学    混合型多流体模型    Mie-Grneisen状态方程    PPM    Riemann问题
文章编号:1001-1455(2006)02-0156-07
修稿时间:2005年1月24日

Piecewise parabolic method for compressible multi-fluid flow with Mie-Grüneisen equation of state
ZHENG Jian-guo,MA Dong-jun,SUN De-jun,YIN Xie-yuan.Piecewise parabolic method for compressible multi-fluid flow with Mie-Grüneisen equation of state[J].Explosion and Shock Waves,2006,26(2):156-162.
Authors:ZHENG Jian-guo  MA Dong-jun  SUN De-jun  YIN Xie-yuan
Institution:1.School of Engineering Science, University of Science and Technology of China, Hefei 230027, Anhui, China
Abstract:A compressible fluid-mixture model based on the volume fraction is introduced and a high-order piecewise parabolic method (PPM) is employed to solve the multi-fluid flow which are characterized by the Mie-Grüneisen equation of state.  The double shock approximation and two level iteration algorithm are used to solve the Riemann problem for general equation of state. A new high resolution scheme is proposed for the mixed type multi-fluid model, which satisfies the principle of oscillation-free for pressure and velocity near the interface between different fluids. For a pure interface problem, the proposed scheme is oscillation-free, and the numerical results also validate that there is no any spurious oscillation in the pressure as well as in velocity profiles on the contact discontinuity while numerical diffusion is limited in two or three cell grids, which is much better than state of the art algorithms. Some numerical experiments and comparisons are presented, and the numerical results show that the new method can simulate the complicated compressible multi-fluid problem such as high pressure ratio Riemann problem, shock-interface interaction and so on.
Keywords:mechanics of explosion  fluid-mixture model  Mie-Grüneisen equation of state  PPM  Riemann problem
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