Athena粒子-气体动力学：方法与收敛性
Particle-Gas Dynamics with Athena: Method and Convergence
摘要：
为了研究原行星盘中气体和固体的动力学以及星子的形成，Athena MHD程序已经扩展到通过气动阻力与气体耦合的粒子运动的积分。我们的粒子-气体混合格式是基于二阶预估-校正方法。仔细处理气体的动量反馈保证了精确的守恒。混合格式在与原行星盘相关的大多数区域是稳定和收敛的。我们描述了一个半隐式积分器从蛙跳方法推广。在没有拖曳力的情况下，它保留了粒子轨道的几何特性。我们还提出了一个全隐式积分器，是无条件稳定的所有制度的粒子-气体耦合。利用我们的混合程序，我们研究了非线性饱和态流动不稳定性的数值收敛性。我们发现，在适当的网格分辨率（无量纲停止时间τ_s=0.1时，每压强长度ηr为128个单元）和相同数量的颗粒和网格单元下，气体流动性质收敛得很好。另一方面，粒子聚集特性仅在更高分辨率下收敛，并且在达到收敛之前，更精细的分辨率导致更强的聚集。最后，我们发现由流动不稳定性引起的粒子输运性质的测量可能会受到约20%的误差。
英文摘要：
The Athena MHD code has been extended to integrates the motion of particles coupled with the gas via aerodynamic drag, in order to study the dynamics of gas and solids in protoplanetary disks and the formation of planetesimals. Our particle-gas hybrid scheme is based on a second order predictor-corrector method. Careful treatment of the momentum feedback on the gas guarantees exact conservation. The hybrid scheme is stable and convergent in most regimes relevant to protoplanetary disks. We describe a semi-implicit integrator generalized from the leap-frog approach. In the absence of drag force, it preserves the geometric properties of a particle orbit. We also present a fully-implicit integrator that is unconditionally stable for all regimes of particle-gas coupling. Using our hybrid code, we study the numerical convergence of the non-linear saturated state of the streaming instability. We find that gas flow properties are well converged with modest grid resolution (128 cells per pressure length ηr for dimensionless stopping time tau_s=0.1), and equal number of particles and grid cells. On the other hand, particle clumping properties converge only at higher resolutions, and finer resolution leads to stronger clumping before convergence is reached. Finally, we find that measurement of particle transport properties resulted from the streaming instability may be subject to error of about 20%.
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