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Volume 30, Issue 5
Consistent Forcing Scheme in the Simplified Lattice Boltzmann Method for Incompressible Flows

Yuan Gao, Liuming Yang, Yang Yu, Guoxiang Hou & Zhongbao Hou

Commun. Comput. Phys., 30 (2021), pp. 1427-1452.

Published online: 2021-10

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  • Abstract

Considering the fact that the lattice discrete effects are neglected while introducing a body force into the simplified lattice Boltzmann method (SLBM), we propose a consistent forcing scheme in SLBM for incompressible flows with external forces. The lattice discrete effects are considered at the level of distribution functions in the present forcing scheme. Consequently, it is more accurate compared with the original forcing scheme used in SLBM. Through Taylor series expansion and Chapman-Enskog (CE) expansion analysis, the present forcing scheme can be proven to recover the macroscopic Navier-Stokes (N-S) equations. Then, the macroscopic equations are resolved through a fractional step technique. Furthermore, the material derivative term is discretized by the central difference method. To verify the results of the present scheme, we simulate with multiple forms of external force interactions including the space- and time-dependent body forces. Hence, the present forcing scheme overcomes the disadvantages of the original forcing scheme and the body force can be accurately imposed in the present scheme even when a coarse mesh is applied while the original scheme fails. Excellent agreements between the analytical solutions and our numerical results can be observed.

  • Keywords

Simplified lattice Boltzmann method, force term implementation, non-uniform body force, ChapmanEnskog analysis, the discrete effect.

  • AMS Subject Headings

76M28

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-1427, author = {Gao , YuanYang , LiumingYu , YangHou , Guoxiang and Hou , Zhongbao}, title = {Consistent Forcing Scheme in the Simplified Lattice Boltzmann Method for Incompressible Flows}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {5}, pages = {1427--1452}, abstract = {

Considering the fact that the lattice discrete effects are neglected while introducing a body force into the simplified lattice Boltzmann method (SLBM), we propose a consistent forcing scheme in SLBM for incompressible flows with external forces. The lattice discrete effects are considered at the level of distribution functions in the present forcing scheme. Consequently, it is more accurate compared with the original forcing scheme used in SLBM. Through Taylor series expansion and Chapman-Enskog (CE) expansion analysis, the present forcing scheme can be proven to recover the macroscopic Navier-Stokes (N-S) equations. Then, the macroscopic equations are resolved through a fractional step technique. Furthermore, the material derivative term is discretized by the central difference method. To verify the results of the present scheme, we simulate with multiple forms of external force interactions including the space- and time-dependent body forces. Hence, the present forcing scheme overcomes the disadvantages of the original forcing scheme and the body force can be accurately imposed in the present scheme even when a coarse mesh is applied while the original scheme fails. Excellent agreements between the analytical solutions and our numerical results can be observed.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0058}, url = {http://global-sci.org/intro/article_detail/cicp/19935.html} }
TY - JOUR T1 - Consistent Forcing Scheme in the Simplified Lattice Boltzmann Method for Incompressible Flows AU - Gao , Yuan AU - Yang , Liuming AU - Yu , Yang AU - Hou , Guoxiang AU - Hou , Zhongbao JO - Communications in Computational Physics VL - 5 SP - 1427 EP - 1452 PY - 2021 DA - 2021/10 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2021-0058 UR - https://global-sci.org/intro/article_detail/cicp/19935.html KW - Simplified lattice Boltzmann method, force term implementation, non-uniform body force, ChapmanEnskog analysis, the discrete effect. AB -

Considering the fact that the lattice discrete effects are neglected while introducing a body force into the simplified lattice Boltzmann method (SLBM), we propose a consistent forcing scheme in SLBM for incompressible flows with external forces. The lattice discrete effects are considered at the level of distribution functions in the present forcing scheme. Consequently, it is more accurate compared with the original forcing scheme used in SLBM. Through Taylor series expansion and Chapman-Enskog (CE) expansion analysis, the present forcing scheme can be proven to recover the macroscopic Navier-Stokes (N-S) equations. Then, the macroscopic equations are resolved through a fractional step technique. Furthermore, the material derivative term is discretized by the central difference method. To verify the results of the present scheme, we simulate with multiple forms of external force interactions including the space- and time-dependent body forces. Hence, the present forcing scheme overcomes the disadvantages of the original forcing scheme and the body force can be accurately imposed in the present scheme even when a coarse mesh is applied while the original scheme fails. Excellent agreements between the analytical solutions and our numerical results can be observed.

Yuan Gao, Liuming Yang, Yang Yu, Guoxiang Hou & Zhongbao Hou. (2021). Consistent Forcing Scheme in the Simplified Lattice Boltzmann Method for Incompressible Flows. Communications in Computational Physics. 30 (5). 1427-1452. doi:10.4208/cicp.OA-2021-0058
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