论文标题
零温度硬球气体中的爆炸波：双缩放结构
Blast waves in the zero temperature hard sphere gas: double scaling structure
论文作者
论文摘要
我们研究了在冷气中突然局部释放能量产生的爆炸。具体而言，我们考虑一维硬杆气和二维硬盘气体。对于这个问题，Euler方程的Taylor-Von Neumann-Sedov（TVNS）解决方案具有自相似形式。对于零温度的气体，冲击波保持无限强，因此该溶液无限期地应用。但是，电视解决方案忽略了耗散。我们表明，这在核心区域中是错误的，在二维中，它以$ t^{2/5} $扩展，而冲击波将其传播为$ t^{1/2} $。根据缩放变量$ r/t^{2/5} $描述了一个新的自相似解决方案，而TVNS解决方案描述了核心。我们从Navier-Stokes方程（NS）方程的数值解决方案和分子动力学模拟中证明了这一点。在这两种情况下，NS方程和TVNS解决方案预测的冲击前置位置都与分子动力学模拟预测的相一致。但是，NS方程无法描述缩放函数的近核形式。
We study the blast generated by sudden localized release of energy in a cold gas. Specifically, we consider one-dimensional hard-rod gas and two-dimensional hard disc gas. For this problem, the Taylor-von Neumann-Sedov (TvNS) solution of Euler equations has a self-similar form. The shock wave remains infinitely strong for the zero-temperature gas, so the solution applies indefinitely. The TvNS solution ignores dissipation, however. We show that this is erroneous in the core region which, in two dimensions, expands as $t^{2/5}$ while the shock wave propagates as $t^{1/2}$. A new self-similar solution depending on the scaling variable $r/t^{2/5}$ describes the core, while the TvNS solution describes the bulk. We demonstrate this from a numerical solution of the Navier-Stokes (NS) equations and from molecular dynamics simulations for a gas of hard discs in two dimensions and hard rods in one dimension. In both cases, the shock front position predicted by NS equations and by the TvNS solution agrees with that predicted by molecular dynamics simulations. However, the NS equations fail to describe the near-core form of the scaling functions.
