模拟吸积盘流动的保涡流体动力学格式
A Vorticity-Preserving Hydrodynamical Scheme for Modeling Accretion Disk Flows
摘要：
旋涡、湍流和非定常非层流可能是天体物理盘的突出和重要的动力学特征。然而，这种强非线性现象通常很难精确地模拟，并且通常只能以理想化的形式进行分析处理。在本文中，我们探讨了可压缩的二维流动的演变，使用隐式双时间流体动力学计划，严格保存涡（如果适用于模拟无粘流的开尔文环流定理是适用的）。该算法基于Lerat，Falissard & Side（2007）的工作，后者在陆地应用的背景下提出了该算法，例如直升机旋翼产生的桨叶-涡流相互作用。我们提出了几个测试Lerat等人。的涡度保持的方法，我们已经实现了二阶精度，提供并排比较与其他算法，经常使用的原恒星盘模拟。比较代码包括一个基于显式的二阶范-莱尔平流，一个基于谱方法，另一个实现高阶Goddom求解器。我们的研究结果表明，Lerat等人的算法将是有用的模拟天体物理环境中的旋涡发挥动力学的作用，并在强烈的冲击是没有预期的。
英文摘要：
Vortices, turbulence, and unsteady non-laminar flows are likely both prominent and dynamically important features of astrophysical disks. Such strongly nonlinear phenomena are often difficult, however, to simulate accurately, and are generally amenable to analytic treatment only in idealized form. In this paper, we explore the evolution of compressible two-dimensional flows using an implicit dual-time hydrodynamical scheme that strictly conserves vorticity (if applied to simulate inviscid flows for which Kelvin's Circulation Theorem is applicable). The algorithm is based on the work of Lerat, Falissard & Side (2007), who proposed it in the context of terrestrial applications such as the blade-vortex interactions generated by helicopter rotors. We present several tests of Lerat et al.'s vorticity-preserving approach, which we have implemented to second-order accuracy, providing side-by-side comparisons with other algorithms that are frequently used in protostellar disk simulations. The comparison codes include one based on explicit, second-order van-Leer advection, one based on spectral methods, and another that implements a higher-order Godunov solver. Our results suggest that Lerat et al's algorithm will be useful for simulations of astrophysical environments in which vortices play a dynamical role, and where strong shocks are not expected.
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