Special Session 108: New Developments in porous media

Analysis of a turbulence k-epsilon model with applications in porous media

Hermenegildo B de Oliveira
Universidade do Algarve
Co-Author(s):    Ana Paiva
In this talk we will analyse a one-equation turbulence model of the k-epsilon type that is being used to describe turbulent flows through porous media. The considered equations are in the steady-state and we supplement them with homogeneous Dirichlet boundary conditions. The novelty of the problem relies on the consideration of the classical Navier-Stokes equations with feedback`s 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. For the considered problem, we prove the existence and uniqueness of weak solutions by assuming suitable growth conditions together with monotone conditions on the feedback terms. In this talk we will also address the issue of existence by considering strongly nonlinear feedback terms and the question of partial regularity of the solutions will be analyzed as well.