Wall-layer boundary condition method for laminar and turbulent flows in weakly-compressible SPH

Abstract

A new method of applying the solid wall boundary condition in a weakly compressible Smooth Particle Hydrodynamics (SPH) method is proposed and tested in a few basic benchmark flows. It makes use of approximate equations of motion and the wall similarity for the pressure and the velocity of the flow near solid walls avoiding the use of the particle interpolation formula which otherwise require special treatment for the truncated smoothing region near the boundary. It is intended to be used in the calculation and the simulation of turbulent flows and test calculations have been done with the Reynolds Averaged Navier Stokes (RANS) equations and spatially-filtered equations of motion and continuity equation with appropriate treatment of turbulence effects. The test calculations of fully developed open channel flow without resolving the viscous sublayer and the transient dam break flows without fully resolving the turbulent fluctuations show that the behaviour seen in the corresponding experimental results is reproduced. The present formulation appears to be an alternative boundary condition formulation to be used in the SPH calculation of practical engineering and environmental flows.