论文标题
通过GSIS提高低变异DSMC的融合
Boosting the convergence of low-variance DSMC by GSIS
论文作者
论文摘要
低变义的直接模拟蒙特卡洛（LVDSMC）是模拟低速稀有气流的强大方法。但是，在近乎固定的流动状态下，由于时间步长和空间细胞尺寸的限制，要找到稳态解决方案需要足够的时间。在这里，我们通过将LVDSMC与一般合成迭代方案（GSIS）耦合来消除这些缺陷，该方案允许在流体动力学量表上进行仿真，而不是小得多的动力学量表。作为概念的证明，我们提出了基于Bhatnagar-gross-Krook动力学模型的随机确定性耦合方法。首先，宏观合成方程完全来自动力学方程，该方程不仅包含navier-stokes-stokes-stokes-fourtore关系，而且还包含描述稀疏效应的高阶术语。然后，从LVDSMC中提取高阶项并将其馈入合成方程，以预测比LVDSMC更接近稳态溶液的宏观特性。最后，更新LVDSMC中的模拟颗粒状态以反映宏观特性的变化。结果，稳定状态的收敛性大大加速，并且对单元大小和时间步的限制进行了删除：在模拟了几种规范的稀有气流后，我们证明了LVDSMC-GSIS在近碳流动状态下的计算成本将计算成本降低了两个数量级。
The low-variance direct simulation Monte Carlo (LVDSMC) is a powerful method to simulate low-speed rarefied gas flows. However, in the near-continuum flow regime, due to limitations on the time step and spatial cell size, it takes plenty of time to find the steady-state solution. Here we remove these deficiencies by coupling the LVDSMC with the general synthetic iterative scheme (GSIS) which permits the simulation at the hydrodynamic scale rather than the much smaller kinetic scale. As a proof of concept, we propose the stochastic-deterministic coupling method based on the Bhatnagar-Gross-Krook kinetic model. First, macroscopic synthetic equations are derived exactly from the kinetic equation, which not only contain the Navier-Stokes-Fourier constitutive relation, but also encompass the higher-order terms describing the rarefaction effects. Then, the high-order terms are extracted from LVDSMC and fed into synthetic equations to predict macroscopic properties which are closer to the steady-state solution than LVDSMC. Finally, the state of simulation particles in LVDSMC is updated to reflect the change of macroscopic properties. As a result, the convergence to steady state is greatly accelerated, and the restriction on cell size and the time step are removed: after simulating several canonical rarefied gas flows, we demonstrate that the LVDSMC-GSIS reduces the computational cost by two orders of magnitude in the near-continuum flow regime.
