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Mathematical and Numerical Analysis of an Alternative Well-Posed Two-Layer Turbulence Model

Published online by Cambridge University Press:  15 April 2002

Bijan Mohammadi  and
Guillaume Puigt
Bijan Mohammadi
Affiliation:
University of Montpellier II, Mathematics Department, ACSIOM Laboratory, France. (mohamadi@math.univ-montp2.fr)
Guillaume Puigt
Affiliation:
University of Montpellier II, Mathematics Department, ACSIOM Laboratory , France. (puigt@math.univ-montp2.fr)
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Abstract

In this article, we wish to investigate the behavior of a two-layer k - ε turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable θ that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical aspects of the model are preserved by the new formulation, and in particular, we show how the physicists can help us to prove the existence of a solution of our problem. Finally, we are interested in the Navier-Stokes equations coupled with the modified turbulence model and we show that the alternative model may be preferred to the original one, because of its good properties (existence of a solution of the coupled problems).

Keywords

Incompressible turbulent flowstwo-layer k - ε modelnear-wall treatment.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 6 , November 2001 , pp. 1111 - 1136
Copyright
© EDP Sciences, SMAI, 2001

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