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Semi-Lagrangian lattice Boltzmann method for compressible flows

  • This work introduces a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows (with or without discontinuities). It makes use of a cell-wise representation of the simulation domain and utilizes interpolation polynomials up to fourth order to conduct the streaming step. The SLLBM solver allows for an independent time step size due to the absence of a time integrator and for the use of unusual velocity sets, like a D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the proposed model are shown in diverse example simulations of 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:Preprint
Author:Dominik Wilde, Andreas Krämer, Dirk Reith, Holger Foysi
ArXiv Id:http://arxiv.org/abs/1910.13918
Date of first publication:2019/10/30
Publication status:Published in Phys. Rev. E 101, 053306 (2020), https://doi.org/10.1103/PhysRevE.101.053306
Funding Information:This work was supported by the German Ministry of Education and Research and the Ministry for Culture and Science North Rhine-Westfalia (research grant 13FH156IN6).
Departments, institutes and facilities:Fachbereich Ingenieurwissenschaften und Kommunikation
Dewey Decimal Classification (DDC):5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Entry in this database:2020/04/09