TVD格式在多组分爆炸波计算中的应用

Application of TVD Scheme in the Calculation of Multi-species Blast Waves

该文将原始的高精度TVD格式推广到含多组分的爆炸波的数值计算 ,建立了多组分混合气体的状态方程 ,并推出了特征值和特征向量矩阵。对一维球对称爆炸场 (爆裂球问题 )的数值计算结果表明 :采用文中推广的多组分TVD格式获得的数值结果比在Lagrangian坐标系下用vonNuemann -Richtmyer格式得到的结果更为合理 ,克服了由人工粘性格式计算引起的爆炸波远场超压偏低的不足 ,同时较好地解决了在Euler坐标系下多组分的变比热比γ的问题。

This paper presents a new numerical method on the calculation of blast waves with multi species gas based on the original TVD scheme . The state equation for mixture gas is established and eigenvalues and eigenvector matrices are also given. Numerical results on the blast waves generated by bursting spheres obtained by TVD method in Euler system are more reasonable than those by von Neumann Richtmyer scheme with artificial viscosity in Lagrangian coordinates and by shock wave recovery method. The drawbacks of lower or higher overpressure value in far field given by the above two methods are well overcome by the present method. The flow characteristics of ideal blast wave are more accurately described. Moreover, the problem of multi species with varying gamma in Euler coordinates is also solved.