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Semi-Lagrangian lattice Boltzmann method for compressible flows

  • This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth order are used to attain the off-vertex distribution function values. Differing from the recently introduced Particles on Demand (PoD) method , the method operates in a static, non-moving reference frame. Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance. The SLLBM solver allows for an independent time step size due to the integration along characteristics and for the use of unusual velocity sets, like the D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.

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Document Type:Article
Author:Dominik Wilde, Andreas Krämer, Dirk Reith, Holger Foysi
Parent Title (English):Physical Review E
Article Number:053306
Publisher:American Physical Society
Publishing Institution:Hochschule Bonn-Rhein-Sieg
Date of first publication:2020/05/08
Copyright:©2020 American Physical Society. Published 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.
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
Open access funding:Hochschule Bonn-Rhein-Sieg / Graduierteninstitut
Entry in this database:2020/04/16
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International