二维多相反应流的欧拉数值方法

本文研究二维多相反应流的数值模拟方法.对于非完全流体，考虑两种状态方程：刚性气体状态方程和JWL（Jones-Wilkins-Lee）型的状态方程.针对这些非完全流体，研究一种混合单元物理量重构法，它由单元内的已知物理量出发，应用单元内不同相的物理量之间的关系：混合密度与各自密度之间的关系、及混合内能与各物质内能之间的关系，再由温度与压强平衡条件，建立关于单变量的非线性方程，对所得方程通过"移动跟踪法"求解，得到单元内的压力、温度及声速等.再利用HLLC解法器，求解各个单元边界数值通量，从而构造一种高效的数值方法.数值结果表明：该算法能清晰地捕捉爆轰波的结构特征，胞格排列有序，三波点的特征明显.

Euler Numerical Methods for Reactive Flow with General Equation of States in Two Dimensions

We present an efficient method to simulate reactive flow for general equation of states in two dimensions. Two kinds of nonideal equation of states for compressible fluid model coupling with reactive rate equation are concerned. The important aspect is to deal with mixture of different phase in one cell, which inevitably happens in Euler method for reactive flows. Physical variables such as pressure,velocity and speed of sound in each cell are reconstructed which results in nonlinear algebra equations. They are used to obtain flux by HLLC Riemann solver. Numerical examples of detonation in two dimensions with different equation of states demonstrate accuracy and robustness of the method.