行星SPH模拟中密度间断的处理
Dealing with density discontinuities in planetary SPH simulations
摘要：
在光滑粒子流体力学（SPH）的标准公式中，密度不连续性不能精确建模，因为密度场被平滑地定义为相邻粒子质量的核加权和。例如，在模拟原行星之间的巨大撞击时，这是一个问题，因为行星通常在其表面和不同材料之间的任何内部边界都有密度不连续性。在这些区域中的不适当的密度创建有效地抑制不同材料的颗粒之间的混合的人工力，并且因此，该问题将关键未知的系统误差引入到依赖于SPH模拟的研究中。在这项工作中，我们提出了一种新的，计算成本低的方法，同时处理这两种类型的密度不连续SPH模拟。我们进行标准的流体动力学测试和几个例子巨大的影响模拟，并与标准SPH的结果进行比较。在使用$10^7$粒子模拟的月球形成撞击中，在模拟期间的某个点处，边界处的改进处理影响至少30%的粒子。
英文摘要：
Density discontinuities cannot be precisely modelled in standard formulations of smoothed particles hydrodynamics (SPH) because the density field is defined smoothly as a kernel-weighted sum of neighbouring particle masses. This is a problem when performing simulations of giant impacts between proto-planets, for example, because planets typically do have density discontinuities both at their surfaces and at any internal boundaries between different materials. The inappropriate densities in these regions create artificial forces that effectively suppress mixing between particles of different material and, as a consequence, this problem introduces a key unknown systematic error into studies that rely on SPH simulations. In this work we present a novel, computationally cheap method that deals simultaneously with both of these types of density discontinuity in SPH simulations. We perform standard hydrodynamical tests and several example giant impact simulations, and compare the results with standard SPH. In a simulated Moon-forming impact using $10^7$ particles, the improved treatment at boundaries affects at least 30% of the particles at some point during the simulation.
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