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A Fast Explicit Operator Splitting Method for Passive Scalar Advection

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Abstract

The dispersal and mixing of scalar quantities such as concentrations or thermal energy are often modeled by advection-diffusion equations. Such problems arise in a wide variety of engineering, ecological and geophysical applications. In these situations a quantity such as chemical or pollutant concentration or temperature variation diffuses while being transported by the governing flow. In the passive scalar case, this flow prescribed and unaffected by the scalar. Both steady laminar and complex (chaotic, turbulent or random) time-dependent flows are of interest and such systems naturally lead to questions about the effectiveness of the stirring to disperse and mix the scalar. The development of reliable numerical methods for advection-diffusion equations is crucial for understanding their properties, both physical and mathematical. In this paper, we extend a fast explicit operator splitting method, recently proposed in (A. Chertock, A. Kurganov, G. Petrova, Int. J. Numer. Methods Fluids 59:309–332, 2009), for solving deterministic convection-diffusion equations, to the problems with random velocity fields and singular source terms. A superb performance of the method is demonstrated on several two-dimensional examples.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Alina Chertock

  2. Departments of Mathematics & Physics, University of Michigan, Ann Arbor, MI, 48109-1043, USA

    Charles R. Doering

  3. Department of Applied Mathematics, Tel Aviv University, Tel Aviv, Ramat Aviv, 69978, Israel

    Eugene Kashdan

  4. Department of Mathematics, Tulane University, New Orleans, LA, 70118, USA

    Alexander Kurganov

Authors
  1. Alina Chertock
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  2. Charles R. Doering
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  3. Eugene Kashdan
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  4. Alexander Kurganov
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Correspondence to Alina Chertock.

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Chertock, A., Doering, C.R., Kashdan, E. et al. A Fast Explicit Operator Splitting Method for Passive Scalar Advection. J Sci Comput 45, 200–214 (2010). https://doi.org/10.1007/s10915-010-9381-2

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  • DOI: https://doi.org/10.1007/s10915-010-9381-2

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