On the Reynolds number sensitivity of smoothed particle hydrodynamics

Abstract

This work investigates the Reynolds number sensitivity of the weakly compressible smoothed particle hydrodynamics method. A mode of instability previously reported for Poiseuille flow is systematically analysed for six relevant test cases. We discuss the influence of the presence of physical viscosity, investigate the origin of the instability for the Couette flow example and explore its implications on convergence properties. Moreover, a novel instability of slightly different nature, which arises in pipe flow with expanding diameter, is detected and a qualitative explanation is given. Since both types of instabilities also occur at Reynolds numbers well below the critical value, its origin is seen in high-frequency particle oscillations independent of any effects of turbulence. We further demonstrate for a flow over a sill and a weir that if there is no breakup of the fluid structure at low Reynolds numbers, then energy balance is accurately simulated even at high Reynolds numbers. Finally, the implications of the instability are addressed from a theoretical, computational and practical perspective.