A Chebyshev Collocation Algorithm for the Solution of Advection-diffusion Equations

Pinelli, A.;Benocci, C.;Deville, M.
(1994) 2nd International Conference on Spectral and High Order Methods (ICOSAHOM 92) — Location: MONTPELLIER(France) (22.June.1992)

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  • Pinelli, A.
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  • Benocci, C.
    Author
  • Deville, M.
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Abstract
An original method to precondition Chebyshev collocated advection-diffusion operators is proposed. The preconditioner, based on an upwind finite difference approximation, is tested on one- and two-dimensional problems. The preconditioner behaves efficiently for advection-dominated cases and produces rates of convergence independent of the number of nodes. Finally, an 'ad hoc' designed multi-domain strategy is introduced.
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Pinelli, A., Benocci, C., & Deville, M. (1994). A Chebyshev Collocation Algorithm for the Solution of Advection-diffusion Equations. Computer Methods in Applied Mechanics and Engineering, 116(1-4), 201-210. https://doi.org/10.1016/S0045-7825(94)80024-3 (Original work published 1994)