标题： 双流体尘埃气体在平滑粒子流体力学中的研究：刚性线性阻力的快速隐式算法 显示英文标题

标题： Two-Fluid Dusty Gas in Smoothed Particle Hydrodynamics: Fast and Implicit Algorithm for Stiff Linear Drag

摘要： 模拟尘埃-气体周围盘的动力学对于理解行星形成机制至关重要。 盘中小颗粒的动力学与气体紧密耦合，而较大固体的动力学则解耦。 此外，在盘的某些部分，尘埃的浓度较低（尘埃与气体质量比约为0.01），而在其他部分则可能高得多。 这些因素对盘模拟的数值方法提出了很高的要求。 特别是，当用两种不同的流体模拟气体和尘埃时，显式方法需要非常小的时间步长（必须小于尘埃停止时间$t_{\rm stop}$，在此期间固体粒子的速度与气体速度相等）才能获得解，而一些隐式方法需要高的时间分辨率才能获得可接受的精度。 此外，最近的研究指出，当用不同的粒子集模拟气体和尘埃时，在光滑粒子流体动力学（SPH）中只有高空间分辨率$h<c_{\rm s} t_{\rm stop}$才能保证由于气体和尘埃相互作用导致的数值过耗散的抑制。 为了解决这些问题，我们开发了一种基于以下思路的快速算法：（1）线性（埃普斯坦）阻力的隐式积分，以及（2）局部线性动量的精确守恒。 我们推导了双流体SPH中单分散尘埃-气体的公式，并在具有已知解析解的问题上测试了新方法。 我们发现，由于空间分辨率条件$h<c_{\rm s} t_{\rm stop}$不再需要以获得准确结果，我们的方法在刚性线性阻力情况下是之前开发的双流体SPH方案的一个有前景的替代方案。 显示英文摘要

摘要： Simulation of the dynamics of dust-gas circumstellar discs is crucial in understanding the mechanisms of planet formation. The dynamics of small grains in the disc is stiffly coupled to the gas, while the dynamics of grown solids is decoupled. Moreover, in some parts of the disc the concentration of the dust is low (dust to gas mass ratio is about 0.01), while in other parts it can be much higher. These factors place high requirements on the numerical methods for disc simulations. In particular, when gas and dust are simulated with two different fluids, explicit methods require very small timestep (must be less than dust stopping time $t_{\rm stop}$ during which the velocity of a solid particle is equalized with respect to the gas velocity) to obtain solution, while some implicit methods requires high temporal resolution to obtain acceptable accuracy. Moreover, recent studies underlined that for Smoothed particle hydrodynamics (SPH) when the gas and the dust are simulated with different sets of particles only high spatial resolution $h<c_{\rm s} t_{\rm stop}$ guaranties suppression of numerical overdissipation due to gas and dust interaction. To address these problems, we developed a fast algorithm based on the ideas of (1) implicit integration of linear (Epstein) drag and (2) exact conservation of local linear momentum. We derived formulas for monodisperse dust-gas in two-fluid SPH and tested the new method on problems with known analytical solutions. We found that our method is a promising alternative for the previously developed two-fluid SPH scheme in case of stiff linear drag thanks to the fact that spatial resolution condition $h<c_{\rm s} t_{\rm stop}$ is not required anymore for accurate results.