This paper presents a new computational method for consistent calculation of mass and momentum fluxes in a two-phase flow simulation. The problem of inconsistency of the mass and momentum transfers has been long known in the two-phase flow context. Once the density ratio between fluid phases becomes high, and/or the momentum of one phase differs significantly from that of the other, a decoupling phenomenon causes a non-physical transfer of momentum, rendering most codes unstable. Original works of Rudman [31] have addressed this by proposing a way to couple the mass and momentum flux transport. To ensure this consistency between both fluxes in a staggered configuration, Rudman introduces a finer sub-grid to transport the volum of fluid.In our paper, we present a way to adopt Rudman's approach without this subgrid, but always in a stagerred grid. The method is presented along with validation test cases and example applications, including very demanding momentum-dominated 3D simulations.

In two-phase flow, the presence of inter-phasal surface -the interface -causes additional terms to appear in LES formulation. Those terms were ignored in contemporary works, for the lack of model and because the authors expected them to be of negligible influence. However, it has been recently shown by a priori DNS simulations that the negligibility assumption can be challenged. In the present work, a model for one of the sub-grid two-phase specific terms is proposed, using deconvolution of the velocity field and advection of the interface using that field. Using the model, the term can be included into LES. A brief presentation of the model is followed by numerical tests that assess the model's performance by comparison with a priori DNS results.