### Abstract

Smoothed particle hydrodynamics (SPH) method has been extensively used to simulate unsteady free surface flows. The works dedicated to simulation of unsteady internal flows have been generally performed to study the transient start up of steady flows under constant driving forces and for low Reynolds number regimes. However, most of the fluid flow phenomena are unsteady by nature and at moderate to high Reynolds numbers. In this study, first a benchmark case (transient Poiseuille flow) is simulated to evaluate the ability of SPH to simulate internal transient flows at low and moderate Reynolds numbers (Re= 0.05, 500 and 1500). For this benchmark case, the performance of the two most commonly used formulations for viscous term modeling is investigated, as well as the effect of using the XSPH variant. Some points regarding using the symmetric form for pressure gradient modeling are also briefly discussed. Then, the application of SPH is extended to oscillating flows imposed by oscillating body force (Womersley type flow) and oscillating moving boundary (Stokes' second problem) at different frequencies and amplitudes. There is a very good agreement between SPH results and exact solution even if there is a large phase lag between the oscillating pressure difference and moving boundary and the movement of the SPH particles generated. Finally, a modified formulation for wall shear stress calculations is suggested and verified against exact solutions. In all presented cases, the spatial convergence analysis is performed.

Original language | English |
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Pages (from-to) | 1431-1450 |

Number of pages | 20 |

Journal | Applied Mathematical Modelling |

Volume | 37 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Feb 2013 |

Externally published | Yes |

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### Keywords

- Pressure symmetric formulation
- Smoothed particle hydrodynamics
- Transient and oscillating flows
- Viscosity formulations
- Wall shear stress
- XSPH variant

### ASJC Scopus subject areas

- Applied Mathematics
- Modelling and Simulation

### Cite this

*Applied Mathematical Modelling*,

*37*(3), 1431-1450. https://doi.org/10.1016/j.apm.2012.04.017