动力学气尘绕星引力的模拟：超越爱泼斯坦机制
Simulations of Dynamical Gas-Dust Circumstellar Disks: Going Beyond the Epstein Regime
摘要：
在拱星盘中，尘埃颗粒的大小从亚微米到几厘米不等，而星子的大小则为数百公里。因此，固体和气体之间的气动阻力的各种制度可以在这些磁盘中实现，这取决于晶粒尺寸和速度：爱泼斯坦，斯托克斯和牛顿，以及它们之间的过渡制度。对于在爱泼斯坦体系中运动的小天体，在气体和天体之间建立恒定相对速度所需的时间可能远小于问题的动力学时间尺度-圆盘绕中心天体旋转的时间。此外，尘埃可能集中在圆盘的各个区域，因此有必要考虑尘埃和气体之间的动量传递。它示出，对于气体和单分散尘埃的方程组，一个半隐式的一阶近似计划的时间，其中相间的相互作用是隐式计算的，而其他的力量，如压力梯度和重力计算明确，是适合于激烈的相间的相互作用和计算的阻力在非线性制度的刚性问题。在天体物理模拟中广泛使用的分段阻力系数在某些马赫数和努森数的值下具有不连续性，这些马赫数和努森数在星周圆盘中实现。一个连续的阻力系数，这对应于实验依赖性获得的各种阻力制度。
英文摘要：
In circumstellar disks, the size of dust particles varies from submicron to several centimeters, while planetesimals have sizes of hundreds of kilometers. Therefore, various regimes for the aerodynamic drag between solid bodies and gas can be realized in these disks, depending on the grain sizes and velocities: Epstein, Stokes, and Newton, as well as transitional regimes between them. For small bodies moving in the Epstein regime, the time required to establish the constant relative velocity between the gas and bodies can be much less than the dynamical time scale for the problem - the time for the rotation of the disk about the central body. In addition, the dust may be concentrated in individual regions of the disk, making it necessary to take into account the transfer of momentum between the dust and gas. It is shown that, for a system of equations for gas and monodisperse dust, a semi-implicit first-order approximation scheme in time in which the interphase interaction is calculated implicitly, while other forces, such as the pressure gradient and gravity are calculated explicitly, is suitable for stiff problems with intense interphase interactions and for computations of the drag in non-linear regimes. The piece-wise drag coefficient widely used in astrophysical simulations has a discontinuity at some values of the Mach and Knudsen numbers that are realized in a circumstellar disk. A continuous drag coefficient is presented, which corresponds to experimental dependences obtained for various drag regimes.
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