On Spectral Approximations for the Stability Analysis of Boundary Layers

Abstract

This paper devotes to the approximation of spectral and boundary-value problems arising in the stability analysis of incompressible boundary layers. As an alternative to the collocation method with mappings, the Galerkin–collocation method based on Laguerre functions is adopted. A robust numerical implementation of the latter method is discussed. The methods are compared within the stability analysis of the Blasius and Ekman layers. The Galerkin–collocation method demonstrates an exponential convergence rate for scalar stability characteristics, and has a number of advantages.