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arXiv 1808.02867astro-ph.EPastro-ph.SR
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星周湍流模拟中气体与尘埃快速动量传递的数值算法分析

Analysis of Numerical Algorithms for Computing Rapid Momentum Transfers between the Gas and Dust in Simulations of Circumstellar Disks

O. P. Stoyanovskaya, E. I. Vorobyov, V. N. Snytnikov

摘要:

现代数值模拟的尘埃和气体的动力学在拱星盘的方法进行了测试。气体和粉尘被视为可以交换动量的互穿连续介质。气体和尘埃相之间的刚性耦合是典型的,这样的磁盘,与尘埃停止时间远小于特征动力学时间尺度。这就对用于模拟尘埃动力学的方法提出了很高的要求。一个网格,分段抛物方法被用来作为基本算法求解气体动力学方程。针对单分散尘埃的情况,给出了使用各种方法计算动量交换获得的数值解。对激波管问题和声波在气尘介质中的传播问题进行了数值求解。所研究的方法进行比较,在他们的能力与(a)任意(短或长)粉尘停止时间,和(b)任意粉尘浓度的气体(从0.01到1的粉尘与气体的质量比变化)的介质模型。确定了一种用于计算具有无限阶精度的动量交换的方法,该方法使得能够以最小的计算成本满足条件(a)和(b)。一个一阶的方法,在测试计算中显示出类似的结果。结果表明,所提出的单分散粉尘的一阶方法可以扩展到一个制度时,粉尘是多分散的,即,由具有不同停止时间的几个分数表示的状态。本文给出了多分散粉尘中各组分与气体交换动量时的气尘速度计算公式。

英文摘要:

Approaches used in modern numerical simulations of the dynamics of dust and gas in circumstellar disks are tested. The gas and dust are treated like interpenetrating continuous media that can exchange momentum. A stiff coupling between the gas and dust phases is typical for such disks, with the dust stopping time much less than the characteristic dynamical time scale. This imposes high demands on the methods used to simulate the dust dynamics. A grid, piecewise-parabolic method is used as the basic algorithm for solving the gas-dynamical equations. Numerical solutions obtained using various methods to compute the momentum exchanges are presented for the case of monodisperse dust. Numerical solutions are obtained for shock tube problem and the propagation of sound waves in a gas-dust medium. The studied methods are compared in terms of their ability to model media with (a) an arbitrary (short or long) dust stopping time, and (b) an arbitrary dust concentration in the gas (varying the dust to gas mass ratio from 0.01 to 1). A method for computing the momentum exchange with infinite-order accuracy in time is identified, which makes it possible to satisfy the conditions (a) and (b) with minimal computational costs. A first-order method that shows similar results in the test computations is also presented. It is shown that the proposed first-order method for monodisperse dust can be extended to a regime when the dust is polydisperse; i.e., a regime represented by several fractions with different stopping times. Formulas for computing the gas and dust velocities for polydisperse dust with each fraction exchanging momentum with the gas are presented.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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