标题： 光滑粒子流体动力学和磁流体动力学 显示英文标题

标题： Smoothed Particle Hydrodynamics and Magnetohydrodynamics

摘要： 本文介绍了平滑粒子流体动力学和磁流体动力学的理论和实践概述和简介。首先，我们给出了SPH的基础知识，展示了如何从密度估计中自洽地推导出运动方程和能量方程。然后，我们说明如何使用基本的SPH插值公式来解释这些方程，并强调SPH与其他粒子方法之间的方法上的细微差别。在此过程中，我们还批评了关于SPH的一些“都市传说”，特别是认为只需缓慢增加“邻近粒子数”而不是总粒子数就可以获得收敛的想法。我们还讨论了数值不稳定性（如配对不稳定性和拉伸不稳定性的）来源。最后，我们提供了解决SPMHD三个主要问题的实用建议：消除拉伸不稳定性、为MHD激波制定耗散项以及在粒子上强制散度约束，并给出了该领域当前的发展状况。伴随论文的是NDSPMHD SPH代码的首次公开发布，这是一个1、2和3维的代码，设计为SPH/SPMHD算法的测试平台，可用于测试许多想法并运行论文中包含的所有数值示例。 显示英文摘要

摘要： This paper presents an overview and introduction to Smoothed Particle Hydrodynamics and Magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several `urban myths' regarding SPH, in particular the idea that one can simply increase the `neighbour number' more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the NDSPMHD SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper.