On von Karman modeling for turbulent flow near a wall

Mixing-length models are often used by engineers in order to take into account turbulence phenomena in a flow. This kind of model is obtained by adding a turbulent viscosity to the laminar one in Navier–Stokes equations. When the flow is confined between two close walls, von Karman’s model consists of adding a viscosity which depends on the rate of strain multiplied by the square of distance to the wall. In this short paper, we present a mathematical analysis of such modeling. In particular, we explain why von Karman’s model is numerically ill-conditioned when using a finite element method with a small laminar viscosity. Details of analysis can be found in [1], [2].

Keywords

Stokes equations, weighted Sobolev spaces, finite element method

2010 Mathematics Subject Classification

46E35, 65Nxx, 76F55

Full Text (PDF format)

The authors would like to thank the Rio-Tinto Alcan Company for their financial support on this project.

Received 18 December 2017

Accepted 12 April 2019

Published 2 April 2020