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Semi-Lagrangian lattice Boltzmann method for compressible flows.
Phys Rev E. 2020 May; 101(5-1):053306.PR

Abstract

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 [Dorschner, Bösch, and Karlin, Phys. Rev. Lett. 121, 130602 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.130602], the method operates in a static, nonmoving 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 nonuniform grids.

Authors+Show Affiliations

Department of Mechanical Engineering, University of Siegen, Paul-Bonatz-Straβe 9-11, D-57076 Siegen-Weidenau, Germany. Institute of Technology, Resource and Energy-efficient Engineering (TREE), Bonn-Rhein-Sieg University of Applied Sciences, Grantham-Allee 20, D-53757 Sankt Augustin, Germany.National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA.Institute of Technology, Resource and Energy-efficient Engineering (TREE), Bonn-Rhein-Sieg University of Applied Sciences, Grantham-Allee 20, D-53757 Sankt Augustin, Germany. Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, D-53754 Sankt Augustin, Germany.Department of Mechanical Engineering, University of Siegen, Paul-Bonatz-Straβe 9-11, D-57076 Siegen-Weidenau, Germany.

Pub Type(s)

Journal Article

Language

eng

PubMed ID

32575305

Citation

Wilde, Dominik, et al. "Semi-Lagrangian Lattice Boltzmann Method for Compressible Flows." Physical Review. E, vol. 101, no. 5-1, 2020, p. 053306.
Wilde D, Krämer A, Reith D, et al. Semi-Lagrangian lattice Boltzmann method for compressible flows. Phys Rev E. 2020;101(5-1):053306.
Wilde, D., Krämer, A., Reith, D., & Foysi, H. (2020). Semi-Lagrangian lattice Boltzmann method for compressible flows. Physical Review. E, 101(5-1), 053306. https://doi.org/10.1103/PhysRevE.101.053306
Wilde D, et al. Semi-Lagrangian Lattice Boltzmann Method for Compressible Flows. Phys Rev E. 2020;101(5-1):053306. PubMed PMID: 32575305.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Semi-Lagrangian lattice Boltzmann method for compressible flows. AU - Wilde,Dominik, AU - Krämer,Andreas, AU - Reith,Dirk, AU - Foysi,Holger, PY - 2019/11/01/received PY - 2020/04/09/accepted PY - 2020/6/25/entrez PY - 2020/6/25/pubmed PY - 2020/6/25/medline SP - 053306 EP - 053306 JF - Physical review. E JO - Phys Rev E VL - 101 IS - 5-1 N2 - 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 [Dorschner, Bösch, and Karlin, Phys. Rev. Lett. 121, 130602 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.130602], the method operates in a static, nonmoving 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 nonuniform grids. SN - 2470-0053 UR - https://www.unboundmedicine.com/medline/citation/32575305/Semi-Lagrangian_lattice_Boltzmann_method_for_compressible_flows DB - PRIME DP - Unbound Medicine ER -
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