Abstract:
For the three-dimensional incompressible Navier-Stokes equations, we present a formulation featuring velocity, vorticity and helical density as independent variables. We show that mathematically the helical density can be observed as a Lagrange multiplier corresponding to the divergence-free constraint on the vorticity variable. As one possible practical application of this formulation, we consider a time-splitting numerical scheme based on a simple alternating procedure between vorticity - helical density and velocity - Bernoulli pressure systems of equations. In this talk we discuss finite element convergence analysis, stabilization and multiscale aspects of the method, the use of algebraic solvers based on the augmented Lagrangian approach, and relations of the numerical method to some well known turbulence models.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.