Interface retaining coarsening of multiphase flows

The presence of a sharp phase boundary is often the most important feature of multiphase flows and as the flow field is coarsened, or filtered, to generate data for modeling the large-scale flow, retaining the interface can be critical. Here we discuss formal ways to coarsen both the indicator function describing the phase distribution as well as the momentum, using diffusion. While coarsening the phase distribution is relatively straightforward, the momentum can be treated in different ways. We can assume mixed zones on either side of the interface, or we can move momentum with the interface. For disperse flows the latter results in the classic point particle approximation. Diffusing the flow while retaining the interface generally results in a slip at the interface as well as at walls, and except in the simplest cases, retaining the interface requires extending current models for the large-scale flow. We have been exploring how to do that using trajectory modeling (or regression) where we augment the governing equations so that the coarse flow evolves correctly, rather than match the structure of the closure terms. Trajectory modeling only requires data describing the coarse flow and thus should be able to incorporate data from a range of sources, including experiments.