Numerical Modeling Of Two-Phase Flow With Contact Discontinuities

Abstract

When simulating high Reynolds number two-phase flow, boundary layers develop at the interface, which are much thinner compared to the capillary length-scales that are of interest. Resolving such an interface layer is expensive and therefore it is often not resolved in a simulation. Numerically such an underresolved interface layer results in a velocity discontinuity tangential to the interface. We propose to include such tangential velocity discontinuities in our numerical model. This results in a sharp two-fluid model for two-phase flow, where only the interface-normal component of the velocity field is smooth. This condition is implicitly enforced via a new jump condition on the pressure gradient, which we discretize using a multidimensional variant of the ghost fluid method [6]. Results are shown of breaking waves [2] as well as (breaking) waves impacting a solid wall [3] where we compare to state-of-the-art methods [3, 4]. We show that our proposed method is able to accurately simulate high Reynolds number two-phase flow without the need for resolving, or artificially thickening, of the interface layer.

Numerical Modelling of Variability in Liquid Impacts

“…We consider (ϵ, Bo) = (0.55, 10 3 ) which yields a plunging breaker, as illustrated in figs. 7.25 and 7.26 where we show example simulations using our proposed two-velocity model 7 .…”

“…We show a close up of the evolution of this instability in fig. 8.26, where we show the actual PLIC reconstruction of the interface 5 , rather than an iso-contour (the zero level set of the function α − 1 2 ) generated in ParaView, which was used in figs. 8.24 and 8.25.…”

“…13),(3.26),(3.28) and(3.29). Recall from section 3.2.2 that the orientation of a part of the DR ∆f is defined as negative if the face normal n f points into it, and therefore the positively oriented part ∆+ c of the oriented union of the DRs, as given by eq.…”