On the singularly perturbed character of the turbulent free jet and its robust numerical solution

Abstract

SUMMARY We consider a numerical approximation of the classical problem of the turbulent free jet. The same boundary layer equation is used for the laminar jet, but with the introduction of the turbulent viscosity. This viscosity depends on the kinematic momentum and the slenderness parameter and varies in space. Here, the problem under consideration is taken to be singularly perturbed, with the slenderness parameter as the perturbation parameter taking arbitrary values from (0,1]. The effective width of the layer depends on the turbulent viscosity and becomes thinner as the slenderness parameter tends to zero. This singularly perturbed character of the turbulent free jet makes this investigation both unique and exploratory. The problem is solved numerically on a finite subdomain by using boundary conditions obtained from the similarity solution. We construct a robust numerical method on the basis of the piecewise‐uniform meshes condensing in the vicinity of the centre of the jet. By numerical experiments, we show that errors for the computed velocity components do not depend on the perturbation parameter. Copyright © 2011 John Wiley & Sons, Ltd.