MATH Seminar

Title: Accounting for Helicity in 3D NSE Computations
Seminar: Numerical Analysis and Scientific Computing
Speaker: Leo Rebholz of Clemson University
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2009-10-21 at 12:45PM
Venue: W306
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Abstract: It has recently become known that helicity, defined as the mean streamwise vorticity, is a fundamentally important quantity of the 3D Navier-Stokes equations. Helicity is a conserved quantity of inviscid flow, is cascaded jointly with energy through the inertial range, and is physically interpreted to be the degree to which a flow's vortex lines are tangled and intertwined. Until recently however, helicity has been ignored in NSE computations. In this talk I will show how helicity can be more accurately treated in finite element computations of the 3D NSE, which in turn leads to more accurate simulations. I will discuss two numerical schemes: one which enforces helicity preservation by the NSE nonlinearity (to mimic the continuous case) - joint work with Vince Ervin, and a second that solves for helicity directly inside of a velocity-vorticity method - joint work with Maxim Olshanskii. Numerical examples will be given that demonstrate the effectiveness of the methods.