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

Marc Haussmann, Stephan Simonis (), Hermann Nirschl () and Mathias J. Krause ()
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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

International Journal of Modern Physics C (IJMPC), 2019, vol. 30, issue 09, 1-29

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.

Keywords: Decaying homogeneous isotropic turbulence; Taylor–Green vortex; lattice Boltzmann methods; OpenLB; direct numerical simulation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183119500748

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