Smoothed particle hydrodynamics method from a large eddy simulation perspective. Generalization to a quasi-Lagrangian model

The present work deals with some recent developments regarding the inclusion of the Large-Eddy Simulation (LES) in the weakly compressible Smoothed Particle Hydrodynamics (SPH) framework. Previously {see the work of Di Mascio et al. [Phys. Fluids 29, 4 (2017)]}, this goal was achieved by applying a Lagrangian filter to the Navier-Stokes equations for compressible fluids and, then, approximating the differential operators in a SPH fashion. Since the Lagrangian nature of the derived scheme turned out to be an obstacle for accurate simulations of high Reynolds number problems, the above approach is here modified to obtain a quasi-Lagrangian LES-SPH model. This relies on the addition of a small velocity deviation to the actual Lagrangian velocity based on the particle shifting technique and on the inclusion of the tensile instability control technique for eliminating the onset of the tensile instability in the fluid regions characterized by large vorticity and negative pressure. The proposed model is successfully tested in both two-dimensional and three-dimensional frameworks by simulating the evolution of freely decaying turbulence problems and comparing the outputs with the available theoretical results and solutions from other numerical models.