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An efficient iterative solution method for the Chebyshev collocation of advection-dominated transport problems

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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


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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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