## Abstract

This work represents a step toward advancing classical methods of bifurcation analysis in conjunction with very large-scale scientific computing needed to model realistically processes which involve laminar and steady flows of incompressible fluids. A robust method of analysis based on pseudoarclength continuation, Newton's method, and direct solution of linear systems is proposed and applied to the analysis of a representative system of fluid mechanics, namely the tilted lid driven cavity. Accurate solution curves, possessing simple singular points, were computed for Reynolds numbers varying from 0 to 10,000 and for different angles of tilt. The results demonstrate that two-dimensional models with up to 1,000,000 algebraic equations can be studied feasibly using the methods described here with state-of-the-art vector supercomputers.

Original language | English (US) |
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Pages (from-to) | 285-311 |

Number of pages | 27 |

Journal | SIAM Journal on Scientific Computing |

Volume | 22 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2000 |

## Keywords

- Factorization of large unsymmetric sparse matrices
- Incompressible and viscous fluids
- Lid driven cavity
- Navier-Stokes equations
- Parameter continuation
- Path following