Abstract
ABSTRACTThis 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.
Highlights
In 1977 Gingold and Monaghan and Lucy introduced the fully Lagrangian meshless smoothed particle hydrodynamics (SPH) method to solve astrophysical problems like star or galaxy formation
Since both types of instabilities 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, energy balance is accurately simulated even at high Reynolds numbers
Summary
In 1977 Gingold and Monaghan and Lucy introduced the fully Lagrangian meshless smoothed particle hydrodynamics (SPH) method to solve astrophysical problems like star or galaxy formation. Since SPH has been applied to a wide range of problems, predominantly in fluid mechanics, from free surface flows (Monaghan 1994; Ferrari 2010; Gomez-Gesteira et al 2010) to multiphase problems (Colagrossi and Landrini 2003; Aristodemo et al 2010) and transport phenomena (Tartakovsky et al 2007). The principle of SPH is to discretize the fluid into particles, which are moved according to a kernel-smoothed influence of its neighbourhood. Particle interactions are governed by discrete equations, in which derivatives of field variables are expressed in terms of smoothing kernel gradients. Numerical tests are frequently carried out in two dimensions even though the step to 3D is in theory straightforward (Ferrari et al 2009)
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