Opuscula Math. 44, no. 2 (2024), 197-240

Opuscula Mathematica

Parabolic turbulence k-epsilon model with applications in fluid flows through permeable media

Hermenegildo Borges de Oliveira

Abstract. In this work, we study a one-equation turbulence \(k\)-epsilon model that governs fluid flows through permeable media. The model problem under consideration here is derived from the incompressible Navier-Stokes equations by the application of a time-averaging operator used in the \(k\)-epsilon modeling and a volume-averaging operator that is characteristic of modeling unsteady porous media flows. For the associated initial- and boundary-value problem, we prove the existence of suitable weak solutions (average velocity field and turbulent kinetic energy) in the space dimensions of physics interest.

Keywords: turbulence, \(k\)-epsilon modelling, permeable media, existence.

Mathematics Subject Classification: 76F60, 76S05, 35Q35, 35K55, 35A01, 76D03.

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  • Communicated by J.I. Díaz.
  • Received: 2023-06-28.
  • Revised: 2023-08-18.
  • Accepted: 2023-08-23.
  • Published online: 2024-01-15.
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Cite this article as:
Hermenegildo Borges de Oliveira, Parabolic turbulence k-epsilon model with applications in fluid flows through permeable media, Opuscula Math. 44, no. 2 (2024), 197-240, https://doi.org/10.7494/OpMath.2024.44.2.197

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