Chebyshev pseudospectral solution of advection-diffusion equations with mapped finite difference preconditioning (Q1323790)

The paper points out the unsuitability of central or upwind finite differencing in their standard form as preconditioners for the spectral solution of advection-diffusion equations at high Péclet numbers. The authors propose a new Chebyshev pseudospectral algorithm with finite difference preconditioning for the solution of the advection-diffusion equation. It is proposed that for an optimal mapping, first and second order Lagrange polynomials can be used for one- and two-dimensional problems, respectively. The technique allows fast convergence.