Enhancing smoothed particle hydrodynamics for turbulent flow simulation: implementation of the dynamic Smagorinsky model

This study focuses on advancing the Smoothed Particle Hydrodynamics (SPH) method to achieve a more accurate simulation of turbulent flows. SPH is a Lagrangian-based mesh-free method that is widely used in fluid dynamics because of its adaptability to complex geometries and free surfaces. Despite its advantages, challenges such as numerical stability, convergence, boundary condition imposition, and effective turbulence modelling remain. We propose the development of a version of the Dynamic Smagorinsky model and incorporate it into the DualSPHysics code. Implementing the Dynamic Smagorinsky model in SPH presents technical challenges due to the need for double filtering, consistent strain-rate evaluation, and local coefficient stability. The proposed implementation offers considerable improvements in turbulence simulations without incurring excessive computational costs. All modifications have been written in C++. The code can be executed on parallel CPUs using high-performance computing (HPC) clusters. The implemented turbulence model was assessed in three cases: a 3D straight open channel flow, a 3D closed channel with a square cross section and a complex 3D open channel flow with bed vegetation. All flows are characterised by large Reynolds numbers. The Dynamic Smagorinsky model, as implemented in this study, reduced velocity prediction errors near solid boundaries and achieved better alignment with the log-law and experimental data. This offers a promising enhancement to SPH’s capability to handle complex turbulent flows and presents a scalable solution for more reliable fluid dynamics simulations. In addition, this research can be used as a guide for the implementation of any turbulence model in DualSPHysics or any other SPH code.