Molecular Dynamic simulation on hydrodynamic instability of interface due to convergence shock and vortex dynamics

利用分子动力学(MD)模拟研究了收敛激波引起的Richtmyer-Meshkov不稳定性(RMI)和Rayleigh-Taylor不稳定性(RTI)等流体动力学不稳定性的非线性演化。我们开发了一种新的MD程序，用于宏观流体动力学模拟和用于研究具有界面密度跳跃的涡旋动力学的非线性理论。主要结果如下：1.大尺度分子动力学模拟程序我们开发了一种新的大尺度分子动力学模拟程序，该程序具有适合于收敛激波驱动的势垒。对于通过计算机网络连接的许多计算机，如Super SINET，代码是并行化的。提出了一种新的动态域组合方法，该方法根据计算环境动态重构计算域。使用720台计算机和通过超级SINET连接的超级计算机验证了该方法的可扩展性。2.Richtmyer-Meshkov不稳定性的非线性演化。利用MD模拟验证了马赫激波和马赫杆的存在性。还研究了收敛几何中波纹激波的非线性稳定性。还首次在柱面几何中研究了RMI的非线性演化，其中不稳定的界面由于反射激波而发生强烈变形。建立了具有密度差的界面涡流动力学的完全非线性理论。我们研究了气泡和尖峰的非线性增长以及双螺旋结构对密度跃迁和初始涡度的依赖关系。3.瑞利-泰勒不稳定性的非线性演化利用分子动力学模拟表明，在RTI中，由于螺旋涡度的存在，发生了反常扩散。我们还发展了一种非线性理论，在该理论中，气泡及其曲率的渐近非线性增长是密度差的函数。

We have investigated nonlinear evolution of hydrodynamic instabilities, such as the Richtmyer-Meshkov instability(RMI) and the Rayleigh-Taylor instability(RTI) induced by converging shock, with the use of Molecular Dynamic(MD) simulations. We have developed a new MD code for macroscopic hydrodynamic simulations and nonlinear theories for a study of vortex dynamics with density jump at an interface. Main results can be summarized as follows.1.Large scale Molecular Dynamic simulation codeWe have developed a new large scale MD simulation code with a suitable potential barrier for converging shock drive. The code was parallelized for many computers connected through a computer network, such as SUPER SINET. A new dynamic domain composition method was developed, in which computational domains are dynamically reconstructed according computational environment. The scalability of the method was proofed with the use of 720 computers and also super-computers connected through the SUPER SINET.2.Nonlinear evolution of the Richtmyer-Meshkov instability.With the use of the MD simulations existence of Mach shock and Mach stem were examined. Nonlinear stability of a rippled shock in converging geometry was also investigated. Nonlinear evolution of RMI was also studied in a cylindrical geometry for the first time, in which unstable interface is strongly deformed due to reflected shocks. A fully nonlinear theory was developed for vortex dynamics of an interface with density difference. We have shown dependence of nonlinear growth of bubble and spike and double spiral structures on density jumps and initial vorticity.3.Nonlinear evolution of the Rayleigh-Taylor instabilityWe have shown that anomalous diffusion occurs due to the vorticity in the spiral in RTI with the use of MD simulations. We have also developed a nonlinear theory in which asymptotic nonlinear growth of a bubble and its curvature were obtained as a function of density difference.