Simulating Turbulent Mixing from Richtmyer-Meshkov and Rayleigh-Taylor Instabilities in Converging Geometries using Moving Cartesian Grids
Simulating Turbulent Mixing from Richtmyer-Meshkov and Rayleigh-Taylor Instabilities in Converging Geometries using Moving Cartesian Grids
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使用移动笛卡尔网格模拟收敛几何中 Richtmyer-Meshkov 和 Rayleigh-Taylor 不稳定性的湍流混合
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发表时间：
2013
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通讯作者：
V. Thomas
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作者：
P. Woodward;J. Jayayaraj;Pei;Michael R. Knox;D. Porter;Chris L. Fryer;G. Dimonte;C. Joggerst;G. Rockefeller;W. Dai;R. Kares;V. Thomas
采用基于分段抛物方法（PPM）和分段抛物Boltzmann（PPB）格式的流体动力学程序，研究了在惯性约束聚变（ICF）应用中精确模拟理想化试验问题中Richtmyer-Meshkov和Rayleigh-Taylor不稳定性的可行性。试验问题产生的径向收敛因子约为6，用50%混合等值线测量，改编自Youngs的研究。伽马值为5/3的伽马定律气体和完美的圆柱形和球形外边界条件在2-D和3-D的研究。收敛网格细化和对称性保护测试表明，在足够高的网格分辨率精确的数值处理这些理想化的，流体力学的问题是可能的移动笛卡尔网格。模拟是切实可行的，以及针对当今的多核和众核计算设备的代码重组技术。结果是球形的情况下，使用网格的4160和10560细胞计算在美国国家科学基金会的蓝色沃茨持续千万亿次系统在NCSA在伊利诺伊大学的初始扰动。背景和动机精确模拟惯性约束聚变（ICF）舱及其所约束的较轻燃料的一个数量级或更多的径向压缩是具有挑战性的，因为在舱表面处起作用的多个流体动力学不稳定性。利用笛卡尔网格的简单性的数值方案可以受益于相对容易的编码以及非常高的执行速度的潜力。然而，网格的自然拓扑结构并不反映ICF问题的对称性。通过使用更紧密地捕获初始状态的球对称性的网格来解决这一缺陷的数值方案在以可承受的成本产生准确的模拟方面需要处理一组不同的挑战。在这项工作中，我们探讨了潜在的笛卡尔方法，以克服其自然的限制，这种类型的问题，使用非常精细的网格。这种方法通过构造代码实现来实现，以利用网格拓扑在当今的多核和众核计算设备上产生非常高的性能。网格也以同源的方式径向向内移动，以捕捉问题的最基本方面，如果不是它的球形拓扑。在这个初步的研究中，没有自适应网格细化（AMR）。因此，我们的研究可以被理解为提供了一个低估的潜力笛卡尔欧拉方法，以准确地模拟ICF流体动力学的简化，理想化的测试问题如下所述。本研究是[1]中介绍的二维研究的后续研究。
The feasibility of accurate simulations of Richtmyer-Meshkov and Rayleigh-Taylor instabilities in idealized test problems motivated by inertial confinement fusion (ICF) applications has been studied using a hydrodynamics code based on the Piecewise-Parabolic Method (PPM) and the Piecewise-Parabolic Boltzmann (PPB) scheme for multifluid volume fraction advection. Test problems producing radial convergence factors of about 6, as measured with the 50% mixing contour, were adapted from those studied by Youngs. Gamma-law gases with gamma values of 5/3 and perfectly cylindrical and spherical outer boundary conditions were employed in both 2-D and 3-D studies. Convergence under grid refinement and symmetry preservation tests indicate that at sufficiently high grid resolutions accurate numerical treatments of these idealized, hydrodynamics-only problems are possible on moving Cartesian meshes. The simulations are made practical as well by code restructuring techniques targeting today’s multiand many-core computing devices. Results are presented for spherical cases with twoand three-mode initial perturbations using grids of 4160 and 10560 cells computed on the NSF’s Blue Waters sustained petascale system at NCSA at the University of Illinois. Background and Motivation Accurately simulating the radial compression by an order of magnitude or more of an inertial confinement fusion (ICF) capsule and the lighter fuel it confines is challenging because of the multiple hydrodynamic instabilities that come into play at the capsule surfaces. Numerical schemes that exploit the simplicity of a Cartesian mesh can benefit from relative coding ease as well as a potential for very high execution speed. However, the natural topology of the mesh does not reflect the symmetries of the ICF problem. Numerical schemes designed to address this defect by using grids that capture the spherical symmetry of the initial state more closely have a different set of challenges to deal with in producing accurate simulations at affordable cost. In this work, we explore the potential for the Cartesian approach to overcome its natural limitations on this type of problem by the use of very fine grids. This approach is made practical by structuring the code implementation to exploit the grid topology to produce very high performance on today’s multiand many-core computing devices. The grid is also made to move radially inward in a homologous fashion, in order to capture the most basic aspect of the problem, if not its spherical topology. In this initial study, no adaptive mesh refinement (AMR) is introduced. Thus our study can be understood as providing an underestimate of the potential for Cartesian Eulerian approaches to accurately simulate ICF hydrodynamics in the simplified, idealized test problems described below. This study is a follow-on to a 2-D study presented in [1].