Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses Positions Contact Publication 12-CNA-001 Numerical Studies of Homogenization Under a Fast Cellular Flow Gautam Iyer    Department of Mathematical Sciences,    Carnegie Mellon University,    Pittsburgh, PA 15213    gautam@math.cmu.edu Konstantinos C. Zygalakis Mathematical Institute, University of Oxford 24-29 St Giles', OX13LB Abstract: We consider a two dimensional particle diffusing in the presence of a fast cellular flow confined to a finite domain. If the flow amplitude $A$ is held fixed, and the number of cells $L^2 \rightarrow \infty$, then problem homogenizes, and has been well studied. Also well studied is the limit when $L$ is fixed, and $A \rightarrow \infty$. In this case the solution averages along stream lines. The double limit as both the flow amplitude $A \to \infty$ and the number of cells $L^2 \to \infty$ was recently studied [Iyer, Komorowski, Novikov, Ryzhik; 2011], one observes a sharp transition between the homogenization and averaging regimes occurring at $A\approx L^{4}$. This paper numerically studies a few theoretically unresolved aspects of this problem when both $A$ and $L$ are large that were left open in [IKNR; 2011] using the numerical method devised in [Pavliotis, Stuart, Zygalakis; 2009]. Our treatment of the numerical method uses recent developments in the theory of modified equations for numerical integrators of SDEs [Zygalakis; 2011]. Get the paper in its entirety as Back to CNA Publications