A mapping method for distributive mixing with diffusion: Interplay between chaos and diffusion in time-periodic sine flow

Conor P. Schlick*, Ivan C. Christov, Paul B. Umbanhowar, Julio M. Ottino, Richard M. Lueptow

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We present an accurate and efficient computational method for solving the advection-diffusion equation in time-periodic chaotic flows. The method uses operator splitting, which allows the advection and diffusion steps to be treated independently. Taking advantage of flow periodicity, the advection step is solved using a mapping method, and diffusion is "added" discretely after each iteration of the advection map. This approach results in the construction of a composite mapping matrix over an entire period of the chaotic advection-diffusion process and provides a natural framework for the analysis of mixing. To test the approach, we consider two-dimensional time-periodic sine flow. By comparing the numerical solutions obtained by our method to reference solutions, we find qualitative agreement for large time steps (structure of concentration profile) and quantitative agreement for small time steps (low error). Further, we study the interplay between mixing through chaotic advection and mixing through diffusion leading to an analytical model for the evolution of the intensity of segregation with time. Additionally, we demonstrate that our operator splitting mapping approach can be readily extended to three dimensions.

Original languageEnglish (US)
Article number052102
JournalPhysics of Fluids
Volume25
Issue number5
DOIs
StatePublished - May 20 2013

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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