Pinelli, Alfredo

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Universidad Complutense de Madrid
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Ciencias Matemáticas
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  • Publication
    An efficient iterative solution method for the Chebyshev collocation of advection-dominated transport problems
    (Society for Industrial and Applied Mathematics, 1996) Pinelli, Alfredo; Couzy, W.; Deville, M. O.; Benocci, C.
    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.