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Volume 27, Issue 1
Burnett Order Stress and Spatially-Dependent Boundary Conditions for the Lattice Boltzmann Method

Timothy Reis

DOI: 10.4208/cicp.OA-2018-0229

Commun. Comput. Phys., 27 (2020), pp. 167-197.

Published online: 2019-10

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  • Abstract

Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method. The accuracy of the method with complicated spatially-dependent boundary conditions for stress and velocity is investigated using the regularized lid-driven cavity flow. The complete set of boundary conditions, which involve gradients evaluated at the boundaries, are implemented locally. A recently-derived collision operator with modified equilibria and velocity-dependent collision rates to reduce the defect in Galilean invariance is also investigated. Numerical results are in excellent agreement with existing benchmark data and exhibit second-order convergence. The lattice Boltzmann stress field is studied and shown to depart significantly from the Newtonian viscous stress when the ratio of Mach to Reynolds numbers is not negligibly small.

  • Keywords

Lattice Boltzmann method, moment based boundary conditions, Burnett stress, regularized cavity.

  • AMS Subject Headings

65Z05, 76A05, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

T.Reis@greenwich.ac.uk (Timothy Reis)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-167, author = {Reis , Timothy}, title = {Burnett Order Stress and Spatially-Dependent Boundary Conditions for the Lattice Boltzmann Method}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {1}, pages = {167--197}, abstract = {

Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method. The accuracy of the method with complicated spatially-dependent boundary conditions for stress and velocity is investigated using the regularized lid-driven cavity flow. The complete set of boundary conditions, which involve gradients evaluated at the boundaries, are implemented locally. A recently-derived collision operator with modified equilibria and velocity-dependent collision rates to reduce the defect in Galilean invariance is also investigated. Numerical results are in excellent agreement with existing benchmark data and exhibit second-order convergence. The lattice Boltzmann stress field is studied and shown to depart significantly from the Newtonian viscous stress when the ratio of Mach to Reynolds numbers is not negligibly small.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0229}, url = {http://global-sci.org/intro/article_detail/cicp/13318.html} }
TY - JOUR T1 - Burnett Order Stress and Spatially-Dependent Boundary Conditions for the Lattice Boltzmann Method AU - Reis , Timothy JO - Communications in Computational Physics VL - 1 SP - 167 EP - 197 PY - 2019 DA - 2019/10 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2018-0229 UR - https://global-sci.org/intro/article_detail/cicp/13318.html KW - Lattice Boltzmann method, moment based boundary conditions, Burnett stress, regularized cavity. AB -

Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method. The accuracy of the method with complicated spatially-dependent boundary conditions for stress and velocity is investigated using the regularized lid-driven cavity flow. The complete set of boundary conditions, which involve gradients evaluated at the boundaries, are implemented locally. A recently-derived collision operator with modified equilibria and velocity-dependent collision rates to reduce the defect in Galilean invariance is also investigated. Numerical results are in excellent agreement with existing benchmark data and exhibit second-order convergence. The lattice Boltzmann stress field is studied and shown to depart significantly from the Newtonian viscous stress when the ratio of Mach to Reynolds numbers is not negligibly small.

Reis , Timothy. (2019). Burnett Order Stress and Spatially-Dependent Boundary Conditions for the Lattice Boltzmann Method. Communications in Computational Physics. 27 (1). 167-197. doi:10.4208/cicp.OA-2018-0229
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