A hybrid R-LES-SPH model for numerical simulation of hydrodynamic problems with violent free-surface flows

Abstract

This paper proposes a novel hybrid R-LES-SPH model for numerical analysis of hydrodynamic problems involving violent free-surface flows. In this model, while viscous diffusion is imposed by a Large Eddy Simulation (LES) formulation in the Lagrangian framework with integrating into the dissipation limiter of the Riemann-SPH (RSPH) model, density diffusion is by a diffusive term connected with Roe’s approximate Riemann solver with dynamic reconstruction. The present hybrid approximation aims to ensure numerically stable analyses with smooth pressure fields, without introducing excessive energy dissipation. In the proposed model, enhanced Particle Shifting (PS) and Volume Conservation Shifting (VCS) schemes are implemented to prevent irregular particle distribution and volume conservation issues faced in the Smoothed Particle Hydrodynamics (SPH) simulations. The solution accuracy and energy conservation properties of the proposed R-LES-SPH model are investigated using several benchmark cases. The proposed model computations are compared with experimental and analytical solutions together with the RSPH and δ-LES-SPH computations. The results showed that the proposed R-LES-SPH model offers more stable and accurate computations with a smoother pressure field and similar energy conservation properties compared to the δ-LES-SPH model. In addition to this, it is observed that the proposed model prevents excessive numerical dissipation with more realistic calculations of viscous forces compared to the RSPH model.