半拉格朗日方法中SPH的隐式积分：在微类星体吸积盘模拟中的应用
Implicit integrations for SPH in Semi-Lagrangian approach: application to the accretion disc modelling in a microquasar
摘要：
当前流体动力学中的显式积分技术受到时间步长级数的Courant-Friedrichs-Lewy条件的深刻限制，该条件基于所采用的空间分辨率以及计算域中的运动速度或信号传输速度之间的最大值。欧拉隐式积分技术，即使更耗时，也可以允许执行稳定的计算流体动力学，付出计算中相对较大的不准确性的代价，而不遭受这种严格的时间限制。本文提出了一种简单有效的方法，用于求解粘性Navier-Stokes流的自由拉格朗日光滑粒子流体动力学（SPH）隐式积分问题。应用SPH方法模拟了双星系统中大质量黑洞周围的吸积盘，并与传统的显式积分方法得到的结果进行了比较。一些一维和二维的关键测试进行了讨论，以检查该技术的有效性。
英文摘要：
Current explicit integration techniques in fluid dynamics are deeply limited by the Courant-Friedrichs-Lewy condition of the time step progression, based on the adopted spatial resolution coupled with the maximum value between the kinetic velocity or the signal transmission speed in the computational domain. Eulerian implicit integration techniques, even though more time consuming, can allow to perform stable computational fluid dynamics paying the price of a relatively larger inaccuracy in the calculations, without suffering such a strict temporal limitation. In this paper, we present a simple and effective scheme to perform Free Lagrangian Smooth Particle Hydrodynamics (SPH) implicit integrations in Semi-Lagrangian approach without any Jacobian matrix inversion operations for viscous Navier-Stokes flows. Applications to SPH accretion disc simulation around a massive black hole (MBH) in a binary stellar system are shown, together with the comparison to the same results obtained according to the traditional explicit integration techniques. Some 1D and 2D critical tests are also discussed to check the validity of the technique.
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