Numerical simulations of diffusion in cellular flows at high Péclet numbers

Yuliya Gorb, Dukjin Nam, Alexei Novikov

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Abstract

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 [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.

Original languageEnglish (US)
Pages (from-to)75-92
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume15
Issue number1
DOIs
Publication statusPublished - Jan 1 2011

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All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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