### Abstract

This paper presents a finite difference technique for solving incompressible turbulent free surface fluid flow problems. The closure of the time-averaged Navier-Stokes equations is achieved by using the two-equation eddy-viscosity model: the high-Reynolds k- (standard) model, with a time scale proposed by Durbin; and a low-Reynolds number form of the standard k- model, similar to that proposed by Yang and Shih. In order to achieve an accurate discretization of the non-linear terms, a second/third-order upwinding technique is adopted. The computational method is validated by applying it to the flat plate boundary layer problem and to impinging jet flows. The method is then applied to a turbulent planar jet flow beneath and parallel to a free surface. Computations show that the high-Reynolds k- model yields favourable predictions both of the zero-pressure-gradient turbulent boundary layer on a flat plate and jet impingement flows. However, the results using the low-Reynolds number form of the k- model are somewhat unsatisfactory.

Original language | English |
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Pages (from-to) | 347-375 |

Number of pages | 28 |

Journal | International Journal for Numerical Methods in Fluids |

Volume | 44 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 2004 |

### Keywords

- averaged Navier-Stokes equations
- finite difference
- turbulent free surface flow
- higher-order upwind bounded scheme
- two-equation k-eddy-viscosity model

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## Cite this

Ferreira, V. G., Mangiavacchi, N., Tomé, M. F., Castelo, A., Cuminato, J. A., & McKee, S. (2004). Numerical simulation of turbulent free surface flow with two-equation k-e eddy-viscosity models.

*International Journal for Numerical Methods in Fluids*,*44*(4), 347-375. https://doi.org/10.1002/fld.641