## Abstract

A method which uses only the velocity components as primitive variables is described for solution of the incompressible unsteady Navier-Stokes equations. The method involves the multiplication of the primitive variable-based Navier-Stokes equations with the unit normal vector of finite volume elements and the integration of the resulting equations along the boundaries of four-node quadrilateral finite volume elements. Therefore, the pressure term is eliminated from the governing equations and any difficulty associated with pressure or vorticity boundary conditions is avoided. The equations are discretized on four-node quadrilateral finite volume elements by using the second-order-accurate central finite differences with the mid-point integral rule in space and the first-order-accurate backward finite differences in time. The resulting system of algebraic equations is solved in coupled form using a direct solver. As a test case, an impulsively accelerated lid-driven cavity flow in a square enclosure is solved in order to verify the accuracy of the present method.

Original language | English |
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Pages (from-to) | 199-203 |

Number of pages | 5 |

Journal | International Journal of Computational Fluid Dynamics |

Volume | 17 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jun 2003 |

Externally published | Yes |

### Funding

The author would like to acknowledge the encouragement and helpful suggestions from Robert Owens. The author would also like to thank Christophe Migeon for providing his original particle-streak images for an impulsively accelerated lid-driven square cavity problem. The author was supported by the Swiss National Science Foundation Grant Number 21-61865.00 for part of this project.

Funders | Funder number |
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Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung | 21-61865.00 |

## Keywords

- Cavity flow
- Incompressible flow
- Unsteady flow
- Velocity formulation
- Viscous flow