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Direct numerical simulation of decaying homogeneous isotropic turbulence — numerical experiments on stability, consistency and accuracy of distinct lattice Boltzmann methods

Author

Listed:
  • Marc Haussmann

    (Lattice Boltzmann Research Group, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany)

  • Stephan Simonis

    (Lattice Boltzmann Research Group, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany)

  • Hermann Nirschl

    (Institute for Mechanical Process Engineering and Mechanics, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany)

  • Mathias J. Krause

    (Lattice Boltzmann Research Group, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany)

Abstract

Stability, consistency and accuracy of various lattice Boltzmann schemes are investigated by means of numerical experiments on decaying homogeneous isotropic turbulence (DHIT). Therefore, the Bhatnagar–Gross–Krook (BGK), the entropic lattice Boltzmann (ELB), the two-relaxation-time (TRT), the regularized lattice Boltzann (RLB) and the multiple-relaxation-time (MRT) collision schemes are applied to the three-dimensional Taylor–Green vortex, which represents a benchmark case for DHIT. The obtained turbulent kinetic energy, the energy dissipation rate and the energy spectrum are compared to reference data. Acoustic and diffusive scaling is taken into account to determine the impact of the lattice Mach number. Furthermore, three different Reynolds numbers Re=800, Re=1600 and Re=3000 are considered. BGK shows instabilities, when the mesh is highly underresolved. The diverging simulations for MRT are ascribed to a strong lattice Mach number dependency. Despite the fact that the ELB modifies the bulk viscosity, it does not mimic a turbulence model. Therefore, no significant increase of stability in comparison to BGK is observed. The TRT “magic parameter” for DHIT at moderate Reynolds numbers is estimated with respect to the energy contribution. Stability and accuracy of the TRT scheme is found to be similar to BGK. For small lattice Mach numbers, the RLB scheme exhibits lowered energy contribution in the dissipation range compared to an analytical model spectrum. Overall, to enhance stability and accuracy, the lattice Mach number should be chosen with respect to the applied collision scheme.

Suggested Citation

  • Marc Haussmann & Stephan Simonis & Hermann Nirschl & Mathias J. Krause, 2019. "Direct numerical simulation of decaying homogeneous isotropic turbulence — numerical experiments on stability, consistency and accuracy of distinct lattice Boltzmann methods," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-29, September.
    • Handle: RePEc:wsi:ijmpcx:v:30:y:2019:i:09:n:s0129183119500748
    DOI: 10.1142/S0129183119500748
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    Cited by:

    1. Albert Mink & Kira Schediwy & Clemens Posten & Hermann Nirschl & Stephan Simonis & Mathias J. Krause, 2022. "Comprehensive Computational Model for Coupled Fluid Flow, Mass Transfer, and Light Supply in Tubular Photobioreactors Equipped with Glass Sponges," Energies, MDPI, vol. 15(20), pages 1-15, October.

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