一种基于特征理论模拟凝聚炸药爆轰的单元中心型Lagrange方法

提出一种数值模拟凝聚炸药爆轰问题的单元中心型Lagrange方法.利用有限体积离散爆轰反应流动方程组，基于双曲型偏微分方程组的特征理论获得离散网格节点的速度与压力，获得的网格节点速度与压力用于更新网格节点位置以及计算网格单元边的数值通量.以这种方式获得的网格节点解是一种"真正多维"的理论解，是一维Godunov格式在二维Riemann问题的推广.有限体积离散得到的爆轰反应流动的半离散系统使用一种显-隐Runge-Kutta格式来离散求解：显式格式处理对流项，隐式格式处理化学反应刚性源项.算例表明，提出的单元中心型Lagrange方法能够较好地模拟凝聚炸药的爆轰反应流动.

A Cell-centered Lagrangian Scheme Based on Characteristics Theory for Condensed Explosive Detonation

We present a cell-centered Lagrangian scheme for numerical simulation of condensed-explosive detonation. It utilizes finite volume method to discrete detonation equations. Velocity and pressure of grid nodes are obtained with characteristics theory of hyperbolic partial differential equations. They are used to update position of grid nodes and calculate numerical flux of grid cells. Solution of grid nodes obtained by characteristics theory is a "genuinely multi-dimensional" theoretical solution, which is a generalization of one-dimensional Godunov scheme in two-dimensional Riemann problem. Semi-discrete system of detonation equations obtained by finite volume scheme is solved with an implicit-explicit Runge-Kutta method. Convection terms are explicitly treated, and stiff source terms of chemical reactions are implicitly treated. The numerical schemes select ZND model for detonation, JWL equations of state for unreacted explosives and detonation products, and use Ignition-Growth model to simulate evolution process in reaction zone. Typical numerical results show that the cell-centered Lagrangian scheme simulates condensed-explosive detonation problems well.