Michael Minion
University of North Carolina at Chapel Hill
Auxilliary Variables and Projection Methods for Incompressible Fluid Dynamics
Abstract: Projection methods are a popular technique for numerically approximating the solution to the incompressible Navier-Stokes equations (and variants thereof) which govern the dynamics of incompressible fluid flow. The projection method strategy is to first compute an intermediate velocity, without respect to the divergence constraint in the governing equations, and then to "project" this intermediate velocity to enforce the divergence constraint. In auxilliary variable methods, one instead approximates the evolution equation of a dynamic variable which does not satisfy a divergence constraint but from which the correct incompressible velocity can be computed through a projection. This approach is a departure from the widely held view of projection methods being equivalent to fractional step schemes, and it allows one to apply higher-order time marching schemes directly to the auxilliary variable equations. This talk will provide a general discussion of auxilliary variables and projection methods, the connection between auxilliary variables and boundary conditions in projection methods, and details of a higher-order numerical implementation based on a deferred corrections strategy. Recent work extending these ideas to the low Mach number limit of the compressible Euler equations will also be presented, as well as a discussion of further cases were auxilliary variable methods appear appropriate.| Zeit: | Freitag, 18. November 2005, 14.15 Uhr (Kaffee/Tee um 15.30) |
| Ort: | FU Berlin, Arnimallee 2-6, Raum 032 im EG |