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Cubature rules for weakly and fully compressible off-lattice Boltzmann methods

  • Off-lattice Boltzmann methods increase the flexibility and applicability of lattice Boltzmann methods by decoupling the discretizations of time, space, and particle velocities. However, the velocity sets that are mostly used in off-lattice Boltzmann simulations were originally tailored to on-lattice Boltzmann methods. In this contribution, we show how the accuracy and efficiency of weakly and fully compressible semi-Lagrangian off-lattice Boltzmann simulations is increased by velocity sets derived from cubature rules, i.e. multivariate quadratures, which have not been produced by the Gauß-product rule. In particular, simulations of 2D shock-vortex interactions indicate that the cubature-derived degree-nine D2Q19 velocity set is capable to replace the Gauß-product rule-derived D2Q25. Likewise, the degree-five velocity sets D3Q13 and D3Q21, as well as a degree-seven D3V27 velocity set were successfully tested for 3D Taylor–Green vortex flows to challenge and surpass the quality of the customary D3Q27 velocity set. In compressible 3D Taylor–Green vortex flows with Mach numbers on-lattice simulations with velocity sets D3Q103 and D3V107 showed only limited stability, while the off-lattice degree-nine D3Q45 velocity set accurately reproduced the kinetic energy provided by literature.

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Document Type:Article
Author:Dominik Wilde, Andreas Krämer, Mario Bedrunka, Dirk Reith, Holger Foysi
Parent Title (English):Journal of Computational Science
Issue:April 2021
Article Number:101355
Place of publication:Amsterdam
Publishing Institution:Hochschule Bonn-Rhein-Sieg
Date of first publication:2021/04/03
Copyright:© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.
Funding:We gratefully acknowledge support for D.W. by German Research Foundation (DFG) project FO 674/17-1. The simulations were performed using the Platform for Scientific Computing at Bonn-Rhein-Sieg University, which is funded by the German Ministry of Education and Research and the Ministry for Culture and Science North Rhine-Westfalia (research grant 13FH156IN6).
Keyword:Compressible; Cubature; Gauss–Hermite quadrature; Lattice Boltzmann Method; Semi-Lagrangian
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 / 51 Mathematik / 510 Mathematik
Open access funding:Hochschule Bonn-Rhein-Sieg / Graduierteninstitut
Entry in this database:2021/04/08
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International