Dutta, Vimala (1993) *Computation of compressible flows: Implicit methods 13; 13;.* In: CFD: Advances and Applications, 1993, Bangalore, India.

## Abstract

The present lecture is mainly concerned with the implicit finite difference technique of Beam and Warming and some of the many variants of this popular and widely used implicit method. The Euler and Navier-Stokes equations for 2-D compressible flows and the implicit time differencing formulae are presented in sections 2 and 3. The implicit, noniterative, approximate factorization, central difference algorithm in delta form is derived in section 4 while section 5 deals with stability and convergence considerations. Next, some salient features of implicit upwind schemes based on flux-vector splitting, and TVD schemes are discussed in section 6. The unfactored implicit relaxation method due to Hanel et al is outlined in section 7. Finally, an implicit finite volume nodal point scheme is presented in section 8. Section 9 presents some examples and results for certain flow problems while section 10 contains some concluding remarks.13; 13;

Item Type: | Conference or Workshop Item (Paper) |
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Uncontrolled Keywords: | Compressible flow;Computational fluid dynamics;Differential equations;Euler equations of motion;Finite difference theory;Navier-stokes equation;Two dimensional flow;Algorithms;Convergence;Flux vector splitting;Numerical stability;TVD schemes |

Subjects: | ENGINEERING > Fluid Mechanics and Thermodynamics |

Division/Department: | Computational and Theoretical Fluid Dynamics Division |

Depositing User: | Mrs Manoranjitha M D |

Date Deposited: | 12 Jan 2007 |

Last Modified: | 24 May 2010 09:54 |

URI: | http://nal-ir.nal.res.in/id/eprint/3821 |

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