Volume 9, Issue 5
Transition Flow with an Incompressible Lattice Boltzmann Method

J. R. Murdock, J. C. Ickes & S. L. Yang

Adv. Appl. Math. Mech., 9 (2017), pp. 1271-1288.

Published online: 2018-05

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  • Abstract

Direct numerical simulations of the transition process from steady laminar to chaotic flow are considered in this study with the relatively new incompressible lattice Boltzmann equation. Numerically, a multiple relaxation time fully incompressible lattice Boltzmann equation is implemented in a 2D driven cavity. Spatial discretization is 2nd-order accurate, and the Kolmogorov length scale estimation based on Reynolds number (Re) dictates grid resolution. Initial simulations show the method to be accurate for steady laminar flows, while higher Re simulations reveal periodic flow behavior consistent with an initial Hopf bifurcation at Re 7,988. Non-repeating flow behavior is observed in the phase space trajectories above Re 13,063, and is evidence of the transition to a chaotic flow regime. Finally, flows at Reynolds numbers above the chaotic transition point are simulated and found with statistical properties in good agreement with literature.

  • Keywords

Multiple relaxation time, lattice Boltzmann, transition, high Reynolds number flow, incompressible flow, lid driven cavity.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-1271, author = {}, title = {Transition Flow with an Incompressible Lattice Boltzmann Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {5}, pages = {1271--1288}, abstract = {

Direct numerical simulations of the transition process from steady laminar to chaotic flow are considered in this study with the relatively new incompressible lattice Boltzmann equation. Numerically, a multiple relaxation time fully incompressible lattice Boltzmann equation is implemented in a 2D driven cavity. Spatial discretization is 2nd-order accurate, and the Kolmogorov length scale estimation based on Reynolds number (Re) dictates grid resolution. Initial simulations show the method to be accurate for steady laminar flows, while higher Re simulations reveal periodic flow behavior consistent with an initial Hopf bifurcation at Re 7,988. Non-repeating flow behavior is observed in the phase space trajectories above Re 13,063, and is evidence of the transition to a chaotic flow regime. Finally, flows at Reynolds numbers above the chaotic transition point are simulated and found with statistical properties in good agreement with literature.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0103}, url = {http://global-sci.org/intro/article_detail/aamm/12200.html} }
TY - JOUR T1 - Transition Flow with an Incompressible Lattice Boltzmann Method JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1271 EP - 1288 PY - 2018 DA - 2018/05 SN - 9 DO - http://dor.org/10.4208/aamm.OA-2016-0103 UR - https://global-sci.org/intro/aamm/12200.html KW - Multiple relaxation time, lattice Boltzmann, transition, high Reynolds number flow, incompressible flow, lid driven cavity. AB -

Direct numerical simulations of the transition process from steady laminar to chaotic flow are considered in this study with the relatively new incompressible lattice Boltzmann equation. Numerically, a multiple relaxation time fully incompressible lattice Boltzmann equation is implemented in a 2D driven cavity. Spatial discretization is 2nd-order accurate, and the Kolmogorov length scale estimation based on Reynolds number (Re) dictates grid resolution. Initial simulations show the method to be accurate for steady laminar flows, while higher Re simulations reveal periodic flow behavior consistent with an initial Hopf bifurcation at Re 7,988. Non-repeating flow behavior is observed in the phase space trajectories above Re 13,063, and is evidence of the transition to a chaotic flow regime. Finally, flows at Reynolds numbers above the chaotic transition point are simulated and found with statistical properties in good agreement with literature.

J. R. Murdock, J. C. Ickes & S. L. Yang. (2020). Transition Flow with an Incompressible Lattice Boltzmann Method. Advances in Applied Mathematics and Mechanics. 9 (5). 1271-1288. doi:10.4208/aamm.OA-2016-0103
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