重访强激波问题：不同几何形状下的收敛和发散激波
Revisiting the Strong Shock Problem: Converging and Diverging Shocks in Different Geometries
摘要：
收敛（内爆）和发散（爆炸）激波的自相似解以前已经在平面、圆柱或球对称中研究过。在这里，我们提供了一个统一的处理这些明显脱节的问题。研究了绝热指数为$γ$、初始密度为$ρ\sim r^{-ω}$的理想气体在强激波作用下的流动。我们在整个参数空间$γ,ω$中刻画了自相似解的特征，并绘制了不同几何之间的联系。我们发现，只有第二类自相似的解决方案是有效的收敛冲击，在某些情况下，收敛冲击可能不会产生一个反射冲击后，其收敛。最后，我们推导出解析近似的相似性指数在整个参数空间。
英文摘要：
Self-similar solutions to converging (implosions) and diverging (explosions) shocks have been studied before, in planar, cylindrical or spherical symmetry. Here we offer a unified treatment of these apparently disconnected problems . We study the flow of an ideal gas with adiabatic index $γ$ with initial density $ρ\sim r^{-ω}$, containing a strong shock wave. We characterize the self-similar solutions in the entirety of the parameter space $γ,ω$, and draw the connections between the different geometries. We find that only type II self-similar solutions are valid in converging shocks, and that in some cases, a converging shock might not create a reflected shock after its convergence. Finally, we derive analytical approximations for the similarity exponent in the entirety of parameter space.
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