Numerical simulations of diffusion in cellular flows at high Péclet numbers

Alexei Novikov, Dukjin Nam, Yuliya Gorb
2010 Discrete and continuous dynamical systems. Series B  
We study numerically the solutions of the steady advection-diffusion 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 → ∞. 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 [24] . This asymptotic model is
more » ... c 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.
doi:10.3934/dcdsb.2011.15.75 fatcat:2ommq26wovgjvhqo2xofme2ijm