光滑粒子流体动力学中的单流体含尘气体
Dusty gas with one fluid in smoothed particle hydrodynamics
摘要：
在一篇配套的论文中，我们已经展示了如何将气体和尘埃描述为由阻力项耦合的两种流体的方程可以重新表述为将系统描述为单一流体混合物。在这里，我们提出了一个数值实现的单流体含尘气体算法使用光滑粒子流体动力学（SPH）。该算法保持了SPH形式主义的守恒性质。特别是，气体和尘埃的总质量、动量、角动量和能量都是精确守恒的。冲击粘度和电导率方面的一般化，以处理相应的两相混合物。该算法的基准对一套全面的问题：dustybox，dustywave，dustyshock和dustyoscill，他们每个人都解决不同的属性的方法。我们比较的性能的单流体算法的标准的两种流体的方法。发现单流体算法解决了双流体算法的两个基本限制：不再可能将灰尘集中到低于气体的分辨率（根据定义，它们具有相同的分辨率），并且在双流体代码中为避免动能的过度阻尼所需的空间分辨率标准h < csts是不必要的。隐式时间步进很简单。因此，该算法对于小颗粒的3D模拟效率高达100亿倍。其他好处包括使用一半的粒子，单个内核和更少的SPH插值。唯一的限制是，它不捕捉多流的灰尘在零耦合的限制，这表明在这种情况下，一个混合的方法可能需要。
英文摘要：
In a companion paper we have shown how the equations describing gas and dust as two fluids coupled by a drag term can be reformulated to describe the system as a single fluid mixture. Here we present a numerical implementation of the one-fluid dusty gas algorithm using Smoothed Particle Hydrodynamics (SPH). The algorithm preserves the conservation properties of the SPH formalism. In particular, the total gas and dust mass, momentum, angular momentum and energy are all exactly conserved. Shock viscosity and conductivity terms are generalised to handle the two-phase mixture accordingly. The algorithm is benchmarked against a comprehensive suit of problems: dustybox, dustywave, dustyshock and dustyoscill, each of them addressing different properties of the method. We compare the performance of the one-fluid algorithm to the standard two-fluid approach. The one-fluid algorithm is found to solve both of the fundamental limitations of the two- fluid algorithm: it is no longer possible to concentrate dust below the resolution of the gas (they have the same resolution by definition), and the spatial resolution criterion h < csts, required in two-fluid codes to avoid over-damping of kinetic energy, is unnecessary. Implicit time stepping is straightforward. As a result, the algorithm is up to ten billion times more efficient for 3D simulations of small grains. Additional benefits include the use of half as many particles, a single kernel and fewer SPH interpolations. The only limitation is that it does not capture multi-streaming of dust in the limit of zero coupling, suggesting that in this case a hybrid approach may be required.
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