Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows

Mohammed Ahmed Boraey

doi:doi:10.11648/j.mma.20170205.11

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Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows

Mohammed Ahmed Boraey

Published in Mathematical Modelling and Applications (Volume 2, Issue 5)

Received: 23 September 2017 Accepted: 24 October 2017 Published: 20 November 2017

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Abstract

The present work investigates the accuracy of the Multiple-relaxation-time Lattice Boltzmann Method (MRT LBM) in the simulation of flows with circulation. The flow in a 2Dlid-driven cavity is simulated using MRT LBM for a wide range of Reynolds numbers (100-1000) to assess its accuracy. The lid-driven cavity flow is selected because it is the standard benchmark problem for the testing of numerical methods. The calculated locations of the primary vortex center in addition to those of the two side vortices (lower-left and lower-right) are compared to the previously published results using different numerical techniques such as finite difference, finite element and single-relaxation-time LBM. The horizontal and vertical velocity profiles are also calculated. The results show that the MRT LBM has a superior accuracy compared to other numerical techniques especially for circulating flows.

Published in	Mathematical Modelling and Applications (Volume 2, Issue 5)
DOI	10.11648/j.mma.20170205.11
Page(s)	47-51
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Multiple-Relaxation-Time, Numerical Accuracy, Lattice Boltzmann Method, Circulating Flow, Lid-Driven Cavity Flow

References

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APA Style

Mohammed Ahmed Boraey. (2017). Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows. Mathematical Modelling and Applications, 2(5), 47-51. https://doi.org/10.11648/j.mma.20170205.11

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ACS Style

Mohammed Ahmed Boraey. Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows. Math. Model. Appl. 2017, 2(5), 47-51. doi: 10.11648/j.mma.20170205.11

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AMA Style

Mohammed Ahmed Boraey. Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows. Math Model Appl. 2017;2(5):47-51. doi: 10.11648/j.mma.20170205.11

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@article{10.11648/j.mma.20170205.11,
  author = {Mohammed Ahmed Boraey},
  title = {Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows},
  journal = {Mathematical Modelling and Applications},
  volume = {2},
  number = {5},
  pages = {47-51},
  doi = {10.11648/j.mma.20170205.11},
  url = {https://doi.org/10.11648/j.mma.20170205.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170205.11},
  abstract = {The present work investigates the accuracy of the Multiple-relaxation-time Lattice Boltzmann Method (MRT LBM) in the simulation of flows with circulation. The flow in a 2Dlid-driven cavity is simulated using MRT LBM for a wide range of Reynolds numbers (100-1000) to assess its accuracy. The lid-driven cavity flow is selected because it is the standard benchmark problem for the testing of numerical methods. The calculated locations of the primary vortex center in addition to those of the two side vortices (lower-left and lower-right) are compared to the previously published results using different numerical techniques such as finite difference, finite element and single-relaxation-time LBM. The horizontal and vertical velocity profiles are also calculated. The results show that the MRT LBM has a superior accuracy compared to other numerical techniques especially for circulating flows.},
 year = {2017}
}

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TY  - JOUR
T1  - Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows
AU  - Mohammed Ahmed Boraey
Y1  - 2017/11/20
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20170205.11
DO  - 10.11648/j.mma.20170205.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 47
EP  - 51
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20170205.11
AB  - The present work investigates the accuracy of the Multiple-relaxation-time Lattice Boltzmann Method (MRT LBM) in the simulation of flows with circulation. The flow in a 2Dlid-driven cavity is simulated using MRT LBM for a wide range of Reynolds numbers (100-1000) to assess its accuracy. The lid-driven cavity flow is selected because it is the standard benchmark problem for the testing of numerical methods. The calculated locations of the primary vortex center in addition to those of the two side vortices (lower-left and lower-right) are compared to the previously published results using different numerical techniques such as finite difference, finite element and single-relaxation-time LBM. The horizontal and vertical velocity profiles are also calculated. The results show that the MRT LBM has a superior accuracy compared to other numerical techniques especially for circulating flows.
VL  - 2
IS  - 5
ER  -

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Author Information

Mohammed Ahmed Boraey

Mechanical Power Engineering Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt

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APA Style

Mohammed Ahmed Boraey. (2017). Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows. Mathematical Modelling and Applications, 2(5), 47-51. https://doi.org/10.11648/j.mma.20170205.11

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ACS Style

Mohammed Ahmed Boraey. Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows. Math. Model. Appl. 2017, 2(5), 47-51. doi: 10.11648/j.mma.20170205.11

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AMA Style

Mohammed Ahmed Boraey. Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows. Math Model Appl. 2017;2(5):47-51. doi: 10.11648/j.mma.20170205.11

Copy | Download

@article{10.11648/j.mma.20170205.11,
  author = {Mohammed Ahmed Boraey},
  title = {Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows},
  journal = {Mathematical Modelling and Applications},
  volume = {2},
  number = {5},
  pages = {47-51},
  doi = {10.11648/j.mma.20170205.11},
  url = {https://doi.org/10.11648/j.mma.20170205.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170205.11},
  abstract = {The present work investigates the accuracy of the Multiple-relaxation-time Lattice Boltzmann Method (MRT LBM) in the simulation of flows with circulation. The flow in a 2Dlid-driven cavity is simulated using MRT LBM for a wide range of Reynolds numbers (100-1000) to assess its accuracy. The lid-driven cavity flow is selected because it is the standard benchmark problem for the testing of numerical methods. The calculated locations of the primary vortex center in addition to those of the two side vortices (lower-left and lower-right) are compared to the previously published results using different numerical techniques such as finite difference, finite element and single-relaxation-time LBM. The horizontal and vertical velocity profiles are also calculated. The results show that the MRT LBM has a superior accuracy compared to other numerical techniques especially for circulating flows.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Assessment of the Accuracy of the Multiple-Relaxation-Time Lattice Boltzmann Method for the Simulation of Circulating Flows
AU  - Mohammed Ahmed Boraey
Y1  - 2017/11/20
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20170205.11
DO  - 10.11648/j.mma.20170205.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 47
EP  - 51
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20170205.11
AB  - The present work investigates the accuracy of the Multiple-relaxation-time Lattice Boltzmann Method (MRT LBM) in the simulation of flows with circulation. The flow in a 2Dlid-driven cavity is simulated using MRT LBM for a wide range of Reynolds numbers (100-1000) to assess its accuracy. The lid-driven cavity flow is selected because it is the standard benchmark problem for the testing of numerical methods. The calculated locations of the primary vortex center in addition to those of the two side vortices (lower-left and lower-right) are compared to the previously published results using different numerical techniques such as finite difference, finite element and single-relaxation-time LBM. The horizontal and vertical velocity profiles are also calculated. The results show that the MRT LBM has a superior accuracy compared to other numerical techniques especially for circulating flows.
VL  - 2
IS  - 5
ER  -

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