We propose a novel Monte-Carlo based ab-initio algorithm for directly computing the statistics for quantities of interest in an immiscible two-phase compressible flow. Our algorithm samples the underlying probability space and evolves these samples with a sharp interface front-tracking scheme. Consequently, statistical information is generated without resorting to any closure assumptions and information about the underlying microstructure is implicitly included. The proposed algorithm is tested on a suite of numerical experiments and we observe that the ab-initio procedure can simulate a variety of flow regimes robustly and converges with respect of refinement of number of samples as well as number of bubbles per volume. The results are also compared with a state-of-the-art discrete equation method to reveal the inherent limitations of existing macroscopic models.

翻译：我们提出了一种基于蒙特卡洛的从头算新算法，用于直接计算不相溶双相可压缩流中感兴趣量的统计特性。该算法对底层概率空间进行采样，并采用尖锐界面追踪格式对这些样本进行演化。因此，无需借助任何封闭假设即可生成统计信息，且底层微结构信息被隐式包含在内。我们通过一系列数值实验对所提算法进行测试，观察到该从头算过程能够稳健地模拟多种流动状态，并且随着样本数量的细化和每体积气泡数量的增加而收敛。此外，结果还与先进的离散方程方法进行了比较，揭示了现有宏观模型的内在局限性。