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Lattice Boltzmann for Advection-Diffusion Problems

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The Lattice Boltzmann Method

Part of the book series: Graduate Texts in Physics ((GTP))

Abstract

After reading this chapter, you will understand how the lattice Boltzmann equation can be adapted from flow problems to advection-diffusion problems with only small changes. These problems include thermal flows, and you will know how to simulate these as two interlinked lattice Boltzmann simulations, one for the flow and one for the thermal advection-diffusion. You will understand how advection-diffusion problems require different boundary conditions from flow problems, and how these boundary conditions may be implemented.

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Notes

  1. 1.

    Of course “conserved” quantities are only conserved in the absence of source terms.

  2. 2.

    Note that D2Q5 and D3Q7 are not sufficient for problems involving anisotropic diffusion with non-zero off-diagonal coefficients [8].

  3. 3.

    D3Q21 is the D3Q15 lattice with six additional vectors (±2, 0, 0)⊤, (0, ±2, 0)⊤ and (0, 0, ±2)⊤.

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Author information

Authors and Affiliations

  1. School of Engineering University of Edinburgh, Edinburgh, UK

    Timm Krüger

  2. Department of Physics, Durham University, Durham, UK

    Halim Kusumaatmaja

  3. Maya Heat Transfer Technologies, Westmount, Québec, Canada

    Alexandr Kuzmin

  4. Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ, USA

    Orest Shardt

  5. IDMEC/IST, University of Lisbon, Lisbon, Portugal

    Goncalo Silva

  6. Acoustics Research Centre, SINTEF ICT, Trondheim, Norway

    Erlend Magnus Viggen

Authors
  1. Timm Krüger
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  2. Halim Kusumaatmaja
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  3. Alexandr Kuzmin
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  4. Orest Shardt
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  5. Goncalo Silva
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  6. Erlend Magnus Viggen
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Krüger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G., Viggen, E.M. (2017). Lattice Boltzmann for Advection-Diffusion Problems. In: The Lattice Boltzmann Method. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-44649-3_8

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