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Volume 34, Issue 3
On Single Distribution Lattice Boltzmann Schemes for the Approximation of Navier Stokes Equations

François Dubois & Pierre Lallemand

DOI: 10.4208/cicp.OA-2022-0185

Commun. Comput. Phys., 34 (2023), pp. 613-671.

Published online: 2023-10

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  • Abstract

In this contribution we study the formal ability of a multi-resolution-times lattice Boltzmann scheme to approximate isothermal and thermal compressible Navier Stokes equations with a single particle distribution. More precisely, we consider a total of 12 classical square lattice Boltzmann schemes with prescribed sets of conserved and nonconserved moments. The question is to determine the algebraic expressions of the equilibrium functions for the nonconserved moments and the relaxation parameters associated to each scheme. We compare the fluid equations and the result of the Taylor expansion method at second order accuracy for bidimensional examples with a maximum of 17 velocities and three-dimensional schemes with at most 33 velocities. In some cases, it is not possible to fit exactly the physical model. For several examples, we adjust the Navier Stokes equations and propose nontrivial expressions for the equilibria.

  • Keywords

Partial differential equations, asymptotic analysis.

  • AMS Subject Headings

76N15, 82C20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-34-613, author = {Dubois , François and Lallemand , Pierre}, title = {On Single Distribution Lattice Boltzmann Schemes for the Approximation of Navier Stokes Equations}, journal = {Communications in Computational Physics}, year = {2023}, volume = {34}, number = {3}, pages = {613--671}, abstract = {

In this contribution we study the formal ability of a multi-resolution-times lattice Boltzmann scheme to approximate isothermal and thermal compressible Navier Stokes equations with a single particle distribution. More precisely, we consider a total of 12 classical square lattice Boltzmann schemes with prescribed sets of conserved and nonconserved moments. The question is to determine the algebraic expressions of the equilibrium functions for the nonconserved moments and the relaxation parameters associated to each scheme. We compare the fluid equations and the result of the Taylor expansion method at second order accuracy for bidimensional examples with a maximum of 17 velocities and three-dimensional schemes with at most 33 velocities. In some cases, it is not possible to fit exactly the physical model. For several examples, we adjust the Navier Stokes equations and propose nontrivial expressions for the equilibria.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0185}, url = {http://global-sci.org/intro/article_detail/cicp/22020.html} }
TY - JOUR T1 - On Single Distribution Lattice Boltzmann Schemes for the Approximation of Navier Stokes Equations AU - Dubois , François AU - Lallemand , Pierre JO - Communications in Computational Physics VL - 3 SP - 613 EP - 671 PY - 2023 DA - 2023/10 SN - 34 DO - http://doi.org/10.4208/cicp.OA-2022-0185 UR - https://global-sci.org/intro/article_detail/cicp/22020.html KW - Partial differential equations, asymptotic analysis. AB -

In this contribution we study the formal ability of a multi-resolution-times lattice Boltzmann scheme to approximate isothermal and thermal compressible Navier Stokes equations with a single particle distribution. More precisely, we consider a total of 12 classical square lattice Boltzmann schemes with prescribed sets of conserved and nonconserved moments. The question is to determine the algebraic expressions of the equilibrium functions for the nonconserved moments and the relaxation parameters associated to each scheme. We compare the fluid equations and the result of the Taylor expansion method at second order accuracy for bidimensional examples with a maximum of 17 velocities and three-dimensional schemes with at most 33 velocities. In some cases, it is not possible to fit exactly the physical model. For several examples, we adjust the Navier Stokes equations and propose nontrivial expressions for the equilibria.

François Dubois & Pierre Lallemand. (2023). On Single Distribution Lattice Boltzmann Schemes for the Approximation of Navier Stokes Equations. Communications in Computational Physics. 34 (3). 613-671. doi:10.4208/cicp.OA-2022-0185
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