Numerical Analysis of a Variational Multiscale Method for Turbulence

Despite efforts of more than centuries, turbulence phenomena is categorized as an unsolved problem. Turbulence is part of everyday's life. The majority of flows of industrial and technological applications are turbulent; natural flows are invariably so. There are many important and interesting physical phenomena which are connected with turbulent flows. Turbulence is observed in natural and engineering applications such as in weather prediction, air pollution, water pollution, aerodynamics and heat exchangers. This work considers an accurate and reliable solutions of turbulent flows. It is concerned with one of the most promising approaches to the numerical simulation of turbulent flows, the subgrid eddy viscosity models. We analyze both continuous and discontinuous finite element approximation of the new subgrid eddy viscosity model. This approach has the advantage that the diffusivity is introduced only on the small scales of the flow. Numerical test shows the new stabilization technique is robust and efficient in solving Navier-Stokes equations for a wide range of Reynolds numbers.