Chebyshev pseudospectral solution of advection-diffusion equations with mapped finite difference preconditioning
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1994
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Elsevier
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Abstract
A new Chebyshev pseudo-spectral algorithm with finite difference preconditioning is proposed for the solution of advection-diffusion equations, A mapping technique is introduced which allows good convergence for any Peclet number both for one-dimensional and two-dimensional problems. Numerical results show that first-order Lagrange polynomials are the optimal mapping procedure for the one-dimensional problem and second-order Lagrange polynomials, for the two-dimensional one.