含SPH-I的含尘气体。算法和测试套件
Dusty gas with SPH - I. Algorithm and test suite
摘要：
本文提出了一种新的光滑粒子流体动力学（SPH）算法来模拟双流体气体和尘埃混合物，系统地解决了多流体系统中的广义SPH密度估计、可变光滑长度项的一致性处理、有限颗粒尺寸、时间步长稳定性、热耦合项以及拖曳算子中核和光滑长度的选择等关键问题。我们发现，使用双峰形内核提高了几百倍的阻力插值的精度相比，使用标准的SPH钟形内核，在没有额外的计算费用。为了基准测试我们的算法，我们已经开发了一套全面的标准化，简单的测试问题的气体和灰尘的混合物：dustybox，dustywave，dustyshock，dustysedov和dustydisc，其中前三个已知的解析解。我们提出了我们的算法对所有这些测试的验证。在这样做时，我们表明，空间分辨率标准Δ <cs ts是一个必要条件，在所有的气体+尘埃代码，成为关键的高阻力（即小停止时间ts），以正确地预测的动态。隐式时间步进和现实的天体物理阻力制度的实施在一个配套文件中解决。
英文摘要：
We present a new algorithm for simulating two-fluid gas and dust mixtures in Smoothed Particle Hydrodynamics (SPH), systematically addressing a number of key issues including the generalised SPH density estimate in multi-fluid systems, the consistent treatment of variable smoothing length terms, finite particle size, time step stability, thermal coupling terms and the choice of kernel and smoothing length used in the drag operator. We find that using double-hump shaped kernels improves the accuracy of the drag interpolation by a factor of several hundred compared to the use of standard SPH bell-shaped kernels, at no additional computational expense. In order to benchmark our algorithm, we have developed a comprehensive suite of standardised, simple test problems for gas and dust mixtures: dustybox, dustywave, dustyshock, dustysedov and dustydisc, the first three of which have known analytic solutions. We present the validation of our algorithm against all of these tests. In doing so, we show that the spatial resolution criterion Δ< cs ts is a necessary condition in all gas+dust codes that becomes critical at high drag (i.e. small stopping time ts) in order to correctly predict the dynamics. Implicit timestepping and the implementation of realistic astrophysical drag regimes are addressed in a companion paper.
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