A Chebyshev spectral method for boundary-layer models

Abstract

Boundary-layers in the atmosphere and ocean often take on the structure of mixed layers bounded by narrow, highly stable regions. Simulation of the movement of such stable regions is a challenging task for the numerical modeler. Here we explore the use of Chebyshev spectral methods. We compare the results of spectral and finite difference methods for a simple one-dimensional test problem with known analytic solution. The results indicate the usefulness of the spectral method in obtaining accurate solutions to boundary-layer problems.