The physical world has a rich diversity of fluid dynamics, ranging from the micron scale to the galactic scale, and varying from high Mach number compressible flows to low Mach number incompressible flows. Large variations in scales, flow properties, and surrounding environments pose many challenges for computations. These issues are particularly important in domains with boundaries. Much of the scientific and technological impact of the Navier-Stokes equations derives from the effect of no-slip boundary conditions in creating physical phenomena such as lift, drag, boundary-layer separation and vortex shedding, for which the behavior of the pressure near boundaries is of great significance. In this talk, I will present new equivalent formulations of Navier-Stokes equations (NSE) better suited for numerical computations. The emphasis will be on the enforcement of imcompressibility and the discovery of intrinsic stability properties that lead to accurate, efficient and practical computations of three dimensional problems.
Coffee and cookies before the presentation at 3:15 pm, and refreshments after the presentation will both be served in Room 128.