ABSTRACT High Mach number shocks are ubiquitous in interstellar turbulence. The Pencil Code is particularly well suited to the study of magnetohydrodynamics in weakly compressible turbulence and the numerical investigation of dynamos because of its high-order advection and time evolution algorithms. However, the high-order algorithms and lack of Riemann solver to follow shocks make it less well suited to handling high Mach number shocks, such as those produced by supernovae (SNe). Here, we outline methods required to enable the code to efficiently and accurately model SNe, using parameters that allow stable simulation of SN-driven turbulence, in order to construct a physically realistic galactic dynamo model. These include the resolution of shocks with artificial viscosity, thermal conductivity and mass diffusion; the correction of the mass diffusion terms and a novel generalisation of the Courant condition to include all source terms in the momentum and energy equations. We test our methods with the numerical solution of the one-dimensional (1D) Riemann shock tube, also extended to a 1D adiabatic shock with parameters and Mach number relevant to SN shock evolution, including shocks with radiative losses. We extend our test with the three-dimensional (3D) numerical simulation of individual SN remnant evolution for a range of ambient gas densities typical of the interstellar medium and compare these to the analytical solutions of Sedov–Taylor (adiabatic) and the snowplough and Cioffi et al. results incorporating cooling and heating processes. We show that our new timestep algorithm leads to linear rather than quadratic resolution dependence as the strength of the artificial viscosity varies, because of the corresponding change in the strength of interzone gradients.

中文翻译：

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模拟超新星驱动的湍流

摘要 高马赫数激波在星际湍流中无处不在。Pencil Code 特别适合弱可压缩湍流中的磁流体动力学研究和发电机的数值研究，因为它具有高阶对流和时间演化算法。然而，高阶算法和缺乏用于跟踪激波的黎曼求解器使其不太适合处理高马赫数激波，例如超新星 (SNe) 产生的激波。在这里，我们概述了使代码能够高效准确地模拟超新星所需的方法，使用允许稳定模拟超新星驱动湍流的参数，以构建物理上真实的银河发电机模型。其中包括通过人工粘度、热导率和质量扩散解决冲击；质量扩散项的校正和 Courant 条件的新推广，以包括动量和能量方程中的所有源项。我们使用一维 (1D) 黎曼激波管的数值解测试我们的方法，还扩展到一维绝热激波，其参数和马赫数与 SN 激波演化相关，包括具有辐射损失​​的激波。我们通过对一系列星际介质典型环境气体密度的单个 SN 残余演化的三维 (3D) 数值模拟来扩展我们的测试，并将这些与 Sedov-Taylor（绝热）以及扫雪机和 Cioffi 的解析解进行比较等。结果结合了冷却和加热过程。