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

Bijan Mohammadi; Guillaume Puigt

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 6, page 1111-1136
  • ISSN: 0764-583X

Abstract

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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).

How to cite

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Mohammadi, Bijan, and Puigt, Guillaume. "Mathematical and Numerical Analysis of an Alternative Well-Posed Two-Layer Turbulence Model." ESAIM: Mathematical Modelling and Numerical Analysis 35.6 (2010): 1111-1136. <http://eudml.org/doc/197393>.

@article{Mohammadi2010,
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). },
author = {Mohammadi, Bijan, Puigt, Guillaume},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Incompressible turbulent flows; two-layer k - ε model; near-wall treatment.; incompressible turbulent flows; two-layer -epsilon model; near-wall treatment},
language = {eng},
month = {3},
number = {6},
pages = {1111-1136},
publisher = {EDP Sciences},
title = {Mathematical and Numerical Analysis of an Alternative Well-Posed Two-Layer Turbulence Model},
url = {http://eudml.org/doc/197393},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Mohammadi, Bijan
AU - Puigt, Guillaume
TI - Mathematical and Numerical Analysis of an Alternative Well-Posed Two-Layer Turbulence Model
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 6
SP - 1111
EP - 1136
AB - 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).
LA - eng
KW - Incompressible turbulent flows; two-layer k - ε model; near-wall treatment.; incompressible turbulent flows; two-layer -epsilon model; near-wall treatment
UR - http://eudml.org/doc/197393
ER -

References

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