Recovering resolvable small scales in hybrid LES-DNS AMR modeling of phase interfaces via spectral differential filtering

In typical Large Eddy Simulations (LES) of turbulent two-phase flows involving immiscible fluids, terms arising due to the discontinuity in density and viscosity at the interface as well as the surface tension force are difficult to model using only filter scale information and are thus often simplified or ignored. An alternative to traditional LES modeling is to avoid the closure problem by using adaptive mesh refinement (AMR) to aggressively refine the mesh from the LES scale to a fully resolved DNS scale at the phase interface such that the interface does not appear in any LES filter. The resulting closure problem is then reduced to two standard single phase sub-grid momentum flux closure problems. However, abrupt mesh resolution and corresponding filter scale transitions in LES suffer from several shortcomings like commutative errors, energy pile-up at fine to coarse mesh transitions, and a slow fill-in of newly resolved small scales at coarse to fine mesh transitions (Piomelli et al., 2006).

To address it, we propose an enrichment procedure for standard prolongation operators based on spectral differential filtering (Bassenne et al., 2019). The approach injects an appropriate amount of newly resolved small scale energy upon mesh refinement and is able to reproduce interfacial curvature statistics of DNS for normal propagating phase interfaces in decaying homogeneous isotropic turbulence.