  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.
