气尘混合物的光滑粒子流体动力学模拟
Smoothed particle hydrodynamics simulations of gas and dust mixtures
摘要：
我们提出了一个“双流体”的实施尘埃在光滑粒子流体动力学（SPH）在测试粒子的限制。该方案能够处理短和长的停止时间，并再现短的摩擦时间限制，这是不正确的处理在其他实现。我们应用新的测试，以验证其准确性和局限性，包括多维测试，以前没有被应用到拖曳耦合尘埃问题，这是特别相关的自引力原行星盘。我们的测试证明了精确模拟气尘混合物的几个关键要求。首先，在标准SPH中，即使气体密度被很好地再现，颗粒抖动也会使粉尘溶液劣化。使用积分梯度，Wendland内核和大量的邻居可以控制这一点，尽管计算成本更高。其次，当有必要限制人工粘度时，我们建议使用Cullen & Dehnen（2010）开关，因为使用$α \sim 0.1$的替代方案可以在尘埃颗粒中产生高达${σ_v} \lesssim 0.3 c_s$的大速度噪声。第三，我们发现，一个准确的尘埃密度估计需要$>400$邻居，因为，不像气体，尘埃粒子不觉得正规化力。这种密度噪声适用于尘埃的所有基于粒子的双流体实现，而不管水力求解器，并可能导致数值诱导的碎片。虽然我们的测试表明，准确的含尘气体模拟是可能的，必须小心，以尽量减少数值噪声的贡献。
英文摘要：
We present a 'two-fluid' implementation of dust in smoothed particle hydrodynamics (SPH) in the test particle limit. The scheme is able to handle both short and long stopping times and reproduces the short friction time limit, which is not properly handled in other implementations. We apply novel tests to verify its accuracy and limitations, including multi-dimensional tests that have not been previously applied to the drag-coupled dust problem and which are particularly relevant to self-gravitating protoplanetary discs. Our tests demonstrate several key requirements for accurate simulations of gas-dust mixtures. Firstly, in standard SPH particle jitter can degrade the dust solution, even when the gas density is well reproduced. The use of integral gradients, a Wendland kernel and a large number of neighbours can control this, albeit at a greater computational cost. Secondly, when it is necessary to limit the artificial viscosity we recommend using the Cullen & Dehnen (2010) switch, since the alternative, using $α \sim 0.1$, can generate a large velocity noise up to ${σ_v} \lesssim 0.3 c_s$ in the dust particles. Thirdly, we find that an accurate dust density estimate requires $>400$ neighbours, since, unlike the gas, the dust particles do not feel regularization forces. This density noise applies to all particle-based two-fluid implementations of dust, irrespective of the hydro solver and could lead to numerically induced fragmentation. Although our tests show accurate dusty gas simulations are possible, care must be taken to minimize the contribution from numerical noise.
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