Date: Thursday, November 5, 2009 4:30 PM
Location: 162 Hollister
Computational fluid dynamics (CFD) has become a popular and widespread tool for analyzing and understanding the complexities of internal and external flows. The first part of this talk presents our recent developments on stabilized finite element methods for the incompressible Navier-Stokes equations. We show the structure of the stabilization terms that are consistently derived based on the variational multiscale ideas, and propose some computationally economic schemes to evaluate the advection part of the stabilization tensor. Performance of the method is evaluated via benchmark problems on stationary and moving meshes, and through application to moving boundary flows and fluid-structure interaction problems.
The second part of the talk extends the variational multiscale ideas to nonlinear stabilization that gives rise to a residual-based turbulence models for Large Eddy Simulation (LES). A significant attribute of the proposed model is that there are no filter functions that invariably cause problems near the walls of the computational domain. Contrary to the ad hoc models employed in traditional LES techniques, the proposed turbulence model is variationally consistent in the sense that if the coarse-scales represent all the features of the flow, then fine-scale terms vanish uniformly. From a code development perspective the residual based turbulence model only involves element level computations thereby resulting in substantial ease of implementation in existing CFD codes. Numerical tests for the turbulent channel flows on cruder meshes are presented and compared with statistics of Direct Numerical Simulations (DNS) that are obtained on substantially refined meshes.
