TY  - JOUR
U1  - Zeitschriftenartikel, wissenschaftlich - begutachtet (reviewed)
A1  - Wilde, Dominik
A1  - Krämer, Andreas
A1  - Bedrunka, Mario
A1  - Reith, Dirk
A1  - Foysi, Holger
T1  - Cubature rules for weakly and fully compressible off-lattice Boltzmann methods
JF  - Journal of Computational Science
N2  - 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.
KW  - Cubature
KW  - Semi-Lagrangian
KW  - Gauss–Hermite quadrature
KW  - Lattice Boltzmann Method
KW  - Compressible
UN  - https://nbn-resolving.org/urn:nbn:de:hbz:1044-opus-53772
SN  - 1877-7503
SS  - 1877-7503
U6  - https://doi.org/10.1016/j.jocs.2021.101355
DO  - https://doi.org/10.1016/j.jocs.2021.101355
VL  - 51
PB  - Elsevier
CY  - Amsterdam
ER  -