撞击坑数值模拟中状态方程替代原则及误差分析

撞击坑是太阳系内大多数类地行星表面的一种重要地质过程，文中介绍了撞击坑形成的机制和撞击坑研究中的数值模拟方法。首先介绍模拟撞击成坑过程的基本理论与策略，着重指出状态方程在数值模拟中具有重要作用。然而，相对于客观世界物质复杂多样，在撞击坑数值模拟中仅有少数物质的状态方程，因此在研究中不可避免地使用其他物质的状态方程进行替换。详细阐述了状态方程替换的概念和原则，即它们的雨贡纽曲线必须相似。其次进一步从理论上分析这种替代过程对物理属性以及溅射速度的影响。最后，开展两个小型撞击坑的数值模拟，靶区分别使用花岗岩和石英岩，模拟结果显示了两次模拟中的峰值压力、温度以及密度的相似性和差异性。这种分析能够有助于行星科学领域的研究，尤其是在目前从月球、火星以及其他星体正在获取越来越多数据的阶段。

The principle of substitution of equation of state and error analysis for crater simulation

Impact cratering is an important surface process on most of the terrestrial planets in solar system. In this paper we described the impact crater formation mechanism, and then introduced the method of numerical simulation for crater study. We first expounded the basic theories and strategies of impact cratering simulation, during which we stressed that Equation of State (EoS) played an important role in the numerical simulation. However, compared to the varieties in the real world, only a few materials’ EoS is available and the substitution is inevitable in craters’ numerical simulation. We elaborated the concept and principle of substituting the EoS with that of another material that their Hugoniot curves should be similar, and we further analyzed the deviation of different physical quantities and ejection velocities from the substitution theoretically. Finally, we carried out numerical simulations to two small craters with targets of granite and quartzite,respectively, and the similarities with the deviations in peak pressure,temperature and densities are directly shown through the results. We think this kind of analyses could support future study in the field of planetary science, especially under the background that much more data would be transmitted from lunar, Mars, and other celestial bodies.