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A lattice Boltzmann relaxation scheme for incompressible fluid flows

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Abstract

Recently, a novel lattice Boltzmann relaxation scheme is introduced for simulating compressible flows in Raghurama Rao et al. (A lattice Boltzmann relaxation scheme (LBRS) for inviscid compressible flows, 2015. arXiv:1504.07034), Deshmukh (lattice Boltzmann relaxation schemes for high-speed flows, PhD Thesis, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 2016). A similar framework of discrete velocities, together with artificial compressibility method (ACM) as another foundation, is introduced here with an aim to simulate incompressible fluid flow equations. The scheme is first introduced for inviscid incompressible flows and applied to quasi-1-D and 2-D incompressible Euler equations. To extend the formulation to viscous flows, Chapman–Enskog expansion is performed and two different approaches are introduced to simulate viscous flows. The new framework, LBRS-ACM, is then tested for standard viscous incompressible flow test cases.

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Authors and Affiliations

  1. IISc Mathematics Initiative (IMI), Indian Institute of Science, Bangalore, India

    Ankit Ruhi

  2. Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India

    S. V. Raghurama Rao

  3. Department of Civil Engineering, Indian Institute of Science, Bangalore, India

    Sekhar Muddu

Authors
  1. Ankit Ruhi
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  2. S. V. Raghurama Rao
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  3. Sekhar Muddu
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Correspondence to S. V. Raghurama Rao.

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Ruhi, A., Raghurama Rao, S.V. & Muddu, S. A lattice Boltzmann relaxation scheme for incompressible fluid flows. Int J Adv Eng Sci Appl Math 14, 34–47 (2022). https://doi.org/10.1007/s12572-022-00320-5

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