A Chebyshev collocation algorithm for the solution of advection—diffusion equations

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.