Resolving high Reynolds numbers in smoothed particle hydrodynamics simulations of subsonic turbulence

Poiseuille flows at two Reynolds numbers (Re) 2.5 × 10−2 and 5.0 are simulated by two different smoothed particle hydrodynamics (SPH) schemes on regular and irregular initial particles' distributions. In the first scheme, the viscous stress is calculated directly by the basic SPH particle approximation, while in the second scheme, the viscous stress is calculated by the combination of SPH particle approximation and finite difference method (FDM). The main aims of this paper are (a) investigating the influences of two different schemes on simulations and reducing the numerical instability in simulating Poiseuille flows discovered by other researchers and (b) investigating whether the similar instability exists in other cases and comparing results with the two viscous stress approximations. For Re = 2.5 × 10−2, the simulation with the first scheme becomes instable after the flow approaches to steady-state. However, this instability could be reduced by the second scheme. For Re = 5.0, no instability for two schemes is found.

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SPH Simulations of Airflow Through a Narrow Constriction

Volume 10: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B, and C ◽

10.1115/imece2008-67673 ◽

2008 ◽

Author(s):

Jaime Klapp ◽

Leonardo Di G. Sigalotti ◽

Eduardo de la Cruz Sanchez

Keyword(s):

Reynolds Numbers ◽

High Accuracy ◽

Experimental Result ◽

Airflow Velocity ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

High Reynolds ◽

Narrow Bridge ◽

Very High ◽

Limiting Value

We simulate the flow of air through a channel with a narrow bridge passage (or throat) at high Reynolds numbers, using the method of Smoothed Particle Hydrodynamics (SPH). The depth of the channel is assumed to be infinite so that the flow is planar. A fully-developed laminar flow with a time increasing velocity is used at the inlet of the channel. The calculation is followed past the point where the airflow velocity becomes sonic (or choked) at the outlet of the throat. We have presented a theoretical model that predicts the well known experimental result that when the flow becomes critical, the pressure drop across the channel reaches a limiting value of ∼ 0.52–0.53. Our numerical calculation reproduced this result with very high accuracy.

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The Effect of Iterative Procedures on the Robustness and Fidelity of Augmented Lagrangian SPH

Symmetry ◽

10.3390/sym13030472 ◽

2021 ◽

Vol 13 (3) ◽

pp. 472

Author(s):

Deniz Can Kolukisa ◽

Murat Ozbulut ◽

Mehmet Yildiz

Keyword(s):

Smoothed Particle Hydrodynamics ◽

Augmented Lagrangian ◽

Reynolds Numbers ◽

Step Size ◽

Time Step ◽

Optimum Time ◽

Time Step Size ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

Spatial Derivatives

The Augmented Lagrangian Smoothed Particle Hydrodynamics (ALSPH) method is a novel incompressible Smoothed Particle Hydrodynamics (SPH) approach that solves Navier–Stokes equations by an iterative augmented Lagrangian scheme through enforcing the divergence-free coupling of velocity and pressure fields. This study aims to systematically investigate the time step size and the number of inner iteration parameters to boost the performance of the ALSPH method. Additionally, the effect of computing spatial derivatives with two alternative schemes on the accuracy of numerical results are also scrutinized. Namely, the first scheme computes spatial derivatives on the updated particle positions at each iteration, whereas the second one employs the updated pressure and velocity fields on the initial particle positions to compute the gradients and divergences throughout the iterations. These two schemes are implemented to the solution of a flow over a circular cylinder at Reynolds numbers of 200 in two dimensions. Initially, simulations are performed in order to determine the optimum time step sizes by utilizing a maximum number of five iterations per time step. Subsequently, the optimum number of inner iterations is investigated by employing the predetermined optimum time step size under the same flow conditions. Finally, the schemes are tested on the same flow problem with different Reynolds numbers using the best performing combination of the aforementioned parameters. It is observed that the ALSPH method can enable one to increase the time step size without deteriorating the numerical accuracy as a consequence of imposing larger ALSPH penalty terms in larger time step sizes, which, overall, leads to improved computational efficiency. When considering the hydrodynamic flow characteristics, it can be stated that two spatial derivative schemes perform very similarly. However, the results indicate that the derivative operation with the updated particle positions produces slightly lower velocity divergence magnitudes at larger time step sizes.

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