A weakly compressible SPH method for RANS simulation of wall-bounded turbulent flows

This paper presents a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method for solving the two-equation Reynolds-Averaged Navier-Stokes (RANS) model. The turbulent wall-bounded flow with or without mild flow separation, a crucial flow pattern in engineering applications, yet rarely explored in the SPH community, is simulated. The inconsistency between the Lagrangian characteristic and RANS model, mainly due to the intense particle shear and near-wall discontinuity, is firstly revealed and addressed by the mainstream and nearwall improvements, respectively. The mainstream improvements, including Adaptive Riemann-eddy Dissipation (ARD) and Limited Transport Velocity Formulation (LTVF), address dissipation incompatibility and turbulent kinetic energy over-prediction issues. The nearwall improvements, such as the particle-based wall model realization, weighted near-wall compensation scheme, and constant $y_p$ strategy, improve the accuracy and stability of the adopted wall model, where the wall dummy particles are still used for future coupling of solid dynamics. Besides, to perform rigorous convergence tests, an level-set-based boundary-offset technique is developed to ensure consistent $y^+$ across different resolutions. The benchmark wall-bounded turbulent cases, including straight, mildly- and strongly-curved, and Half Converging and Diverging (HCD) channels are calculated. Good convergence is, to our best knowledge, firstly achieved for both velocity and turbulent kinetic energy for the SPH-RANS method. All the results agree well with the data from the experiments or simulated by the Eulerian methods at engineering-acceptable resolutions. The proposed method bridges particle-based and mesh-based RANS models, providing adaptability for other turbulence models and potential for turbulent fluid-structure interaction (FSI) simulations.