Iterative Chebeshev pseudo-spectral solver for 2D convection-diffusion equations

Abstract

Iterative implementation of the Chebyshev spectral collocation method as applied to solving 2D convection-diffusion equation is investigated. It is shown that the stabilized biCG iterative methods with preconditioner on the base the finite difference approximation of the Laplace operator implemented by means of the Bartels-Stuart algorithm has rapid convergence but its performance degrades at high Peclet numbers. In the case of iLu preconditioner the convergence suffer from increasing grid size but stable at high Peclet numbers