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

Oliveira Hermenegildo Borges de

Opuscula Mathematica

2024

Vol. 44, no. 2

197--240

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.