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Pinelli, Alfredo and Couzy, W. and Deville, M. O. and Benocci, C.
(1996)
*An efficient iterative solution method for the Chebyshev collocation of advection-dominated transport problems.*
SIAM journal on scientific computing, 17
(3).
pp. 647-657.
ISSN 1064-8275

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Official URL: http://epubs.siam.org/doi/abs/10.1137/S1064827593253835

## Abstract

A new Chebyshev collocation algorithm is proposed for the iterative solution of advection-diffusion problems. The main features of the method lie in the original way in which a finite-difference preconditioner is built and in the fact that the solution is collocated on a set of nodes matching the standard Gauss-Lobatto-Chebyshev set only in the case of pure diffusion problems. The key point of the algorithm is the capability of the preconditioner to represent the high-frequency modes when dealing with advection-dominated problems. The basic idea is developed for a one-dimensional case and is extended to two-dimensional problems. A series of numerical experiments is carried out to demonstrate the efficiency of the algorithm. The proposed algorithm can also be used in the context of the incompressible Navier-Stokes equations.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | advection-diffusion; collocation; Chebyshev; preconditioning; finite difference; staggered grid |

Subjects: | Sciences > Mathematics |

ID Code: | 21923 |

Deposited On: | 17 Jun 2013 11:45 |

Last Modified: | 12 Dec 2018 18:34 |

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