Investigation of mixed spectral and finite difference approximation on the basis of a viscous flow problem in a diffusor

A general approach to derivation of efficient numerical methods based on a mixed spectral and finite difference approximation for problems, whose solutions are smooth in some variables and non-smooth in other variables is considered.
The approach considered is applied to the problem of a viscous liquid flow in a plane diffusor. Properties of the numerical method are investigated on the basis of computational experiments.