## Abstract

The time‐dependent Navier–Stokes equations and the energy balance equation for an incompressible, constant property fluid in the Boussinesq approximation are solved by a least‐squares finite element method based on a velocity–pressure–vorticity–temperature–heat‐flux (u–P–ω–T–q) formulation discretized by backward finite differencing in time. The discretization scheme leads to the minimization of the residual in the l^{2}‐norm for each time step. Isoparametric bilinear quadrilateral elements and reduced integration are employed. Three examples, thermally driven cavity flow at Rayleigh numbers up to 10^{6}, lid‐driven cavity flow at Reynolds numbers up to 10^{4} and flow over a square obstacle at Reynolds number 200, are presented to validate the method.

Original language | English |
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Pages (from-to) | 271-289 |

Number of pages | 19 |

Journal | International Journal for Numerical Methods in Fluids |

Volume | 17 |

Issue number | 4 |

DOIs | |

State | Published - Aug 30 1993 |

## Keywords

- Bqussinesq approximation
- Incompressible flows
- Least‐squares finite element method
- Navier–Stokes equations
- Time‐dependent

## ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics