Fine Scale Interfacial Models for Discrete Multiphase Flows with Convecting Discontinuities

This paper presents a residual-based stabilized formulation for compressible-incompressible multiphase flows on nonoverlapping subdomains with sharp changes in material properties across phase boundaries. The formulation accommodates surface tension effects at the phase boundaries that give rise to jumps in the pressure field. Phase-specific governing equations together with appropriate equations of state are employed in the corresponding subdomains wherein variation in density as a function of pressure is accommodated in the compressible fluid. The new method is endowed with a discontinuity capturing feature that naturally emerges when fine-scale models are embedded with the surface tension term at the discrete interfaces. The method is integrated with the level-set equation to define the evolving interphase interfaces as they traverse through a fixed but otherwise arbitrary Eulerian mesh. The discontinuity capturing feature of the method accurately models steep gradients across the traversing phase boundaries without the need for expensive adaptive remeshings. Surface tension effects that are variationally incorporated in the formulation play an important role in the shape evolution of bubbles and provide flexibility in the modeling of bubble growth, shrinkage, and collapse due to hydrodynamic forces and convective effects. The method effectively models Kelvin-Helmholtz instability, which arises due to shearing velocity across the compressible-incompressible interface between the two fluids that have discontinuous material properties and different governing equations for each of the constituents.