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MRT and TRT Collision Operators

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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 have a solid understanding of the general principles of multiple-relaxation-time (MRT) and two-relaxation-time (TRT) collision operators. You will know how to implement these and how to choose the various relaxation times in order to increase the stability, the accuracy, and the possibilities of lattice Boltzmann simulations.

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Notes

  1. 1.

    In the following we will only explain the force-free algorithm; the inclusion of forces is discussed in Sect. 10.5.

  2. 2.

    Alternatively, because of the orthogonality condition (10.12) one can represent each column of \({\boldsymbol M}^{-1}\) through the corresponding row vector of \({\boldsymbol M}\). We leave this as an exercise for an interested reader.

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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). MRT and TRT Collision Operators. In: The Lattice Boltzmann Method. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-44649-3_10

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