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High-order semi-Lagrangian kinetic scheme for compressible turbulence

  • Turbulent compressible flows are traditionally simulated using explicit Eulerian time integration applied to 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 elegantly circumvents this restriction. Previous lattice Boltzmann methods for compressible flows were mostly restricted to two dimensions due to the enormous number of discrete velocities needed in three dimensions. In contrast, this Rapid Communication demonstrates how cubature rules enhance the SLLBM to yield a three-dimensional velocity set with only 45 discrete velocities. Based on simulations of a compressible Taylor-Green vortex we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques, 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 for the first time to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time step sizes is only dictated by physics, while being decoupled from the spatial discretization.

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Document Type:Preprint
Author:Dominik Wilde, Andreas Krämer, Dirk Reith, Holger Foysi
Number of pages:10
ArXiv Id:http://arxiv.org/abs/2012.05537
Date of first publication:2020/12/10
Publication status:Final version available at Phys. Rev. E 104, 025301, doi:10.1103/PhysRevE.104.025301
Departments, institutes and facilities:Fachbereich Ingenieurwissenschaften und Kommunikation
Institut für Technik, Ressourcenschonung und Energieeffizienz (TREE)
Dewey Decimal Classification (DDC):5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Entry in this database:2020/12/16
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International