семинары
Семинар "Математические модели механики сплошной среды" 04.09. 2018 в 10-30
4 сентября 2018 г. в 10-30 в конференц-зале ИГиЛ СО РАН состоится семинар "Математические модели механики сплошной среды", на котором выступит Hermenegildo Borges de Oliveira (Universidade do Algarve, Portugal)
с докладом «Turbulent flows through porous media»
Аннотация доклада:
We consider a one-equation turbulence model of the k-epsilon
type that governs fluid flows through porous media. The problem is
considered in the steady state and the governing equations are
supplemented 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. By assuming
suitable growth conditions on the feedback's forces field and on the
production term, as well as on the function that describes the rate of
dissipation of the TKE, we will prove the existence of the velocity field
and of the TKE. We will also discuss the issue of existence by assuming
strongly nonlinear feedbacks. The proof of uniqueness is made by assuming
monotonicity conditions on the feedback forces field and on the function
of turbulent dissipation, 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. This talk is based in joint works with Ana Paiva [1,2].
[1] H.B. de Oliveira and A. Paiva. A stationary one-equation turbulent
model with applications in porous media. J. Math. Fluid Mech. 20 (2018),
no. 2, 263-287.
[2] H.B. de Oliveira and A. Paiva. Existence for a one-equation turbulent
model with strong nonlinearities. J. Elliptic Parabol. Equ. 3 (2017), no.
1-2, 65-91.