%0 Journal Article
%A Pinelli, Alfredo
%A Couzy, W.
%A Deville, M. O.
%A Benocci, C.
%T An efficient iterative solution method for the Chebyshev collocation of advection-dominated transport problems
%D 1996
%@ 1064-8275
%U https://hdl.handle.net/20.500.14352/58576
%X 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.
%~