Existence, uniqueness and regularity of solution of the equations of a turbulence model for incompressible fluids

Abstract

The aim of this paper is the mathematical analysis of a system of Partial Differential Equations arising from the Fluid Mechanics. This system governs the motion of the mean velocity and pressure of a turbulent flow, when one uses the turbulence model of Smagorinsky with special boundary conditions, arising from the modeling of the boundary layer. We present some results of existence and uniqueness of solution for both the Steady-State and the Evolution problem. A result of regularity for the Evolution problem is presented too. Finally, we describe briefly the discretization used to solve numerically the system and we show some views of the results obtained

Keywords:

• Nonlinear P.D.E.
• Turbulence Incompressible Navier-Stokes
• Boundary Layers
• Finite Element

AMS(MOS)::

• 35A05
• 35Q10
• 65C20
• 65M60