### Abstract

A numerical simulation scheme of 3D incompressible viscous fluid in a box flow passage is developed to solve Navier-Stokes (N-S) equations by firstly taking fluid-structure interaction (FSI) into account. This numerical scheme with FSI is based on the polynomial differential quadrature (PDQ) approximation technique, in which motions of both the fluid and the solid boundary structures are well described. The flow passage investigated consists of four rectangular plates, of which two are rigid, while another two are elastic. In the simulation the elastic plates are allowed to vibrate subjected to excitation of the time-dependent dynamical pressure induced by the unsteady flow in the passage. Meanwhile, the vibrating plates change the flow pattern by producing many transient sources and sinks on the plates. The effects of FSI on the flow are evaluated by running numerical examples with the incoming flow's Reynolds numbers of 3000, 7000 and 10,000, respectively. Numerical computations show that FSI has significant influence on both the velocity and pressure fields, and the DQ method developed here is effective for modelling 3D incompressible viscous fluid with FSI.

Original language | English |
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Pages (from-to) | 2034-2049 |

Number of pages | 16 |

Journal | Applied Mathematical Modelling |

Volume | 31 |

Issue number | 9 |

Early online date | 3 Nov 2006 |

DOIs | |

Publication status | Published - Sep 2007 |

### Keywords

- three-dimensional viscous flow
- N-S equations
- numerical simulation
- fluid-structure interaction
- differential quadrature method
- Navier-Stokes equations
- liquid-filled pipes
- vibration analysis
- DNS
- models
- number

## Cite this

*Applied Mathematical Modelling*,

*31*(9), 2034-2049. https://doi.org/10.1016/j.apm.2006.08.007