# American Institute of Mathematical Sciences

January  2011, 15(1): 75-92. doi: 10.3934/dcdsb.2011.15.75

## Numerical simulations of diffusion in cellular flows at high Péclet numbers

 1 Department of Mathematics, University of Houston, Houston, TX 77204, United States 2 Department of Mathematics, Ajou University, Suwon 443-749, South Korea 3 Department of Mathematics, Pennsylvania State University, University Park, State College, PA 16802, United States

Received  November 2009 Revised  April 2010 Published  October 2010

We study numerically the solutions of the steady advection-diffu-sion problem in bounded domains with prescribed boundary conditions when the Péclet number Pe is large. We approximate the solution at high, but finite Péclet numbers by the solution to a certain asymptotic problem in the limit Pe $\to \infty$. The asymptotic problem is a system of coupled 1-dimensional heat equations on the graph of streamline-separatrices of the cellular flow, that was developed in [21]. This asymptotic model is implemented numerically using a finite volume scheme with exponential grids. We conclude that the asymptotic model provides for a good approximation of the solutions of the steady advection-diffusion problem at large Péclet numbers, and even when Pe is not too large.
Citation: Yuliya Gorb, Dukjin Nam, Alexei Novikov. Numerical simulations of diffusion in cellular flows at high Péclet numbers. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 75-92. doi: 10.3934/dcdsb.2011.15.75
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