Display Abstract

Title On optimal mixing schemes

Name Julien Dambrine
Country France
Email julien.dambrine@math.univ-poitiers.fr
Submit Time 2014-02-26 04:44:10
Special Session 2: Nonlinear evolution PDEs and interfaces in applied sciences
Optimal stirring is an important issue in chemical engineering. The underlying optimization problem is the following: given a color function $c$ transported with a solenoidal velocity, what is the velocity $(t,X) \rightarrow V(t,X)$ that ensures the quickest mixing ? Of course, the answer depends on : - The definition of the mixing criterion - The energy constraint on the velocity Recent works of Mathew et. al. have shown that a good criterion for measuring the mixing of two fluids in the periodic case is the $H^{-\frac{1}{2}}$ norm. An explicit locally-in-time optimal mixing scheme has been suggested in subsequent works from Lin et. al. In this talk we will investigate this mixing scheme both numerically and through a linear stability analysis, in a framework that is as general as possible. In particular we will show the ill-posedness of the linearized model when the energy constraint on the velocity is taken as the kinetic energy, and the well-posedness when this energy constraint is the viscous dissipation energy.