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High-order semi-Lagrangian kinetic scheme for compressible turbulence

  • Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time-step size. Exploiting the Lagrangian nature of the Boltzmann equation’s material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this restriction. While many lattice Boltzmann methods for compressible flows were restricted to two dimensions due to the enormous number of discrete velocities in three dimensions, the SLLBM uses only 45 discrete velocities. Based on compressible Taylor-Green vortex simulations we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques other than the filtering introduced by the interpolation, even when the time-step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time-step sizes is dictated by physics rather than spatial discretization.

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Document Type:Article
Author:Dominik Wilde, Andreas Krämer, Dirk Reith, Holger Foysi
Parent Title (English):Physical Review E
Article Number:025301
First Page:1
Last Page:15
Publisher:American Physical Society
Publishing Institution:Hochschule Bonn-Rhein-Sieg
Date of first publication:2021/08/06
Copyright:©2021 American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license.
Funding:This work was supported by the German Ministry of Education and Research and the Ministry for Culture and Science North Rhine-Westfalia (research Grant No. 13FH156IN6). D.W. is supported by German Research Foundation (DFG) Project No. FO 674/17-1.
Keyword:Compressible flows; Fluid Dynamics; Kinetic theory; Lattice-Boltzmann methods; Navier-Stokes equation; Statistical Physics; Turbulence
Departments, institutes and facilities:Fachbereich Ingenieurwissenschaften und Kommunikation
Institut für Technik, Ressourcenschonung und Energieeffizienz (TREE)
EI-HPC - Enabling Infrastructure for HPC-Applications (DE/BMBF/13FH156IN6)
Dewey Decimal Classification (DDC):5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Entry in this database:2021/08/19
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International