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Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 2, pp 263–287 | Cite as

A Stationary One-Equation Turbulent Model with Applications in Porous Media

  • H. B. de Oliveira
  • A. Paiva
Article
  • 88 Downloads

Abstract

A one-equation turbulent model is studied in this work in the steady-state and with homogeneous Dirichlet boundary conditions. The considered problem generalizes two distinct approaches that are being used with success in the applications to model different flows through porous media. The novelty of the problem relies on the consideration of the classical Navier–Stokes equations with a feedback forces field, whose presence in the momentum equation will affect the equation for the turbulent kinetic energy (TKE) with a new term that is known as the production and represents the rate at which TKE is transferred from the mean flow to the turbulence. By assuming suitable growth conditions on the feedback forces field and on the function that describes the rate of dissipation of the TKE, as well as on the production term, we will prove the existence of the velocity field and of the TKE. The proof of their uniqueness is made by assuming monotonicity conditions on the feedback forces field and on the turbulent dissipation function, together with a condition of Lipschitz continuity on the production term. The existence of a unique pressure, will follow by the application of a standard version of de Rham’s lemma.

Keywords

Turbulence k-epsilon modelling Porous media Existence Uniqueness 

Mathematics Subject Classification

76F60 76S05 35J57 35D30 76D03 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.FCTUniversidade do AlgarveFaroPortugal
  2. 2.CMAFCIOUniversidade de LisboaLisbonPortugal

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