Large eddy simulation within the smoothed particle hydrodynamics: Applications to multiphase flows

In this paper, the large eddy simulation (LES) model introduced in the smoothed particle hydrodynamics (SPH) by Di Mascio et al. [Phys. Fluids 29, 035102 (2017)] and called δ-LES-SPH, is extended to treat multiphase flows. This is achieved by modifying the multiphase δ-SPH by Hammani et al. [Comput. Methods Appl. Mech. Eng. 368, 113189 (2020)] by switching the viscous and density diffusion constants to dynamic variables evaluated as turbulence closure terms. The equation for energy conservation is also written for the presented model. The validation is performed for two-dimensional problems, by comparison with other established SPH solvers, with a finite volume method solver based on the turbulence closure corresponding to that adopted for the Lagrangian scheme, and with experimental data. The first test case investigated is a modified Taylor-Green vortex in which the introduction of macro-bubbles of a lighter fluid phase inside the domain is considered. In the second test case, a more violent problem involving wave breaking and splashing dynamics is analyzed. In the final test, the dynamic of a sloshing problem is reproduced. An analysis of turbulence resolution is conducted by considering modeled and resolved turbulent kinetic energies, as well as viscous dissipation and turbulent viscosity dissipation.