Abstract
We consider here the approximation of a generalized Stokes problem by spectral methods in the collocation form. This problem is of particular interest when Navier-Stokes equations for viscous compressible flows are investigated. We also analyze a coupling of a viscous model with an inviscid one; precisely, we split the computational domain in two parts and in one of them we eliminate the viscous coefficient from the Stokes equations. Such an approach can be worthwhile in the study of compressible fluids around rigid profiles with critical layers. Finally we consider some numerical results with the aim of showing the excellent accuracy of the spectral approximations, as well as the efficiency of an iterative algorithm that we propose in order to alternate viscous and inviscid numerical solvers.
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