A unified wall-boundary condition for the lattice boltzmann method and its application to force evaluation

San-Yih Lin, Y. H. Chin, F. L. Yang, J. F. Lin, J. J. Hu, C. S. Chen, S. H. Hsieh

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A unified wall-boundary condition for the pressure-based lattice Boltzmann method (LBM) is proposed. The present approach is developed from the direct-forcing technique in the immersed boundary method and is derived from the equilibrium pressure distribution function. The proposed method can handle many kinds of wall boundaries, such as fixed wall and moving wall boundaries, in the same way. It is found that the new method has the following advantages: (1) simple in concept and easy to implement, (2) higher-order accuracy, (3) mass conservation, and (4) a stable and good convergence rate. Based on this wall-boundary condition, if a solid wall is immersed in a fluid, then by applying Gauss's theorem, the formulas for computing the force and torque acting on the solid wall from fluid flow are derived from the volume integrals over the solid volume instead of from the surface integrals over the solid surface. Based on the pressure-based LBM, inlet and outlet boundary conditions are also proposed. The order of accuracy of the proposed boundary condition is demonstrated with the errors of the velocity field, wall stress, and gradients of velocity and pressure. The steady flow past a circular cylinder is simulated to demonstrate the efficiency and capabilities of the proposed unified method.

Original languageEnglish
Pages (from-to)55-68
Number of pages14
JournalJournal of Mechanics
Volume31
Issue number1
DOIs
Publication statusPublished - 2015 Feb 1

Fingerprint

Lattice Boltzmann Method
Boundary conditions
boundary conditions
evaluation
Evaluation
Immersed Boundary Method
High Order Accuracy
Surface integral
Mass Conservation
Equilibrium Distribution
Pressure Distribution
Circular Cylinder
Steady flow
Circular cylinders
Steady Flow
Pressure distribution
Velocity Field
Forcing
Gauss
Torque

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics

Cite this

Lin, San-Yih ; Chin, Y. H. ; Yang, F. L. ; Lin, J. F. ; Hu, J. J. ; Chen, C. S. ; Hsieh, S. H. / A unified wall-boundary condition for the lattice boltzmann method and its application to force evaluation. In: Journal of Mechanics. 2015 ; Vol. 31, No. 1. pp. 55-68.
@article{b04809c8ce9249af93d392c45e6be9af,
title = "A unified wall-boundary condition for the lattice boltzmann method and its application to force evaluation",
abstract = "A unified wall-boundary condition for the pressure-based lattice Boltzmann method (LBM) is proposed. The present approach is developed from the direct-forcing technique in the immersed boundary method and is derived from the equilibrium pressure distribution function. The proposed method can handle many kinds of wall boundaries, such as fixed wall and moving wall boundaries, in the same way. It is found that the new method has the following advantages: (1) simple in concept and easy to implement, (2) higher-order accuracy, (3) mass conservation, and (4) a stable and good convergence rate. Based on this wall-boundary condition, if a solid wall is immersed in a fluid, then by applying Gauss's theorem, the formulas for computing the force and torque acting on the solid wall from fluid flow are derived from the volume integrals over the solid volume instead of from the surface integrals over the solid surface. Based on the pressure-based LBM, inlet and outlet boundary conditions are also proposed. The order of accuracy of the proposed boundary condition is demonstrated with the errors of the velocity field, wall stress, and gradients of velocity and pressure. The steady flow past a circular cylinder is simulated to demonstrate the efficiency and capabilities of the proposed unified method.",
author = "San-Yih Lin and Chin, {Y. H.} and Yang, {F. L.} and Lin, {J. F.} and Hu, {J. J.} and Chen, {C. S.} and Hsieh, {S. H.}",
year = "2015",
month = "2",
day = "1",
doi = "10.1017/jmech.2014.80",
language = "English",
volume = "31",
pages = "55--68",
journal = "Journal of Mechanics",
issn = "1727-7191",
publisher = "Cambridge University Press",
number = "1",

}

A unified wall-boundary condition for the lattice boltzmann method and its application to force evaluation. / Lin, San-Yih; Chin, Y. H.; Yang, F. L.; Lin, J. F.; Hu, J. J.; Chen, C. S.; Hsieh, S. H.

In: Journal of Mechanics, Vol. 31, No. 1, 01.02.2015, p. 55-68.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A unified wall-boundary condition for the lattice boltzmann method and its application to force evaluation

AU - Lin, San-Yih

AU - Chin, Y. H.

AU - Yang, F. L.

AU - Lin, J. F.

AU - Hu, J. J.

AU - Chen, C. S.

AU - Hsieh, S. H.

PY - 2015/2/1

Y1 - 2015/2/1

N2 - A unified wall-boundary condition for the pressure-based lattice Boltzmann method (LBM) is proposed. The present approach is developed from the direct-forcing technique in the immersed boundary method and is derived from the equilibrium pressure distribution function. The proposed method can handle many kinds of wall boundaries, such as fixed wall and moving wall boundaries, in the same way. It is found that the new method has the following advantages: (1) simple in concept and easy to implement, (2) higher-order accuracy, (3) mass conservation, and (4) a stable and good convergence rate. Based on this wall-boundary condition, if a solid wall is immersed in a fluid, then by applying Gauss's theorem, the formulas for computing the force and torque acting on the solid wall from fluid flow are derived from the volume integrals over the solid volume instead of from the surface integrals over the solid surface. Based on the pressure-based LBM, inlet and outlet boundary conditions are also proposed. The order of accuracy of the proposed boundary condition is demonstrated with the errors of the velocity field, wall stress, and gradients of velocity and pressure. The steady flow past a circular cylinder is simulated to demonstrate the efficiency and capabilities of the proposed unified method.

AB - A unified wall-boundary condition for the pressure-based lattice Boltzmann method (LBM) is proposed. The present approach is developed from the direct-forcing technique in the immersed boundary method and is derived from the equilibrium pressure distribution function. The proposed method can handle many kinds of wall boundaries, such as fixed wall and moving wall boundaries, in the same way. It is found that the new method has the following advantages: (1) simple in concept and easy to implement, (2) higher-order accuracy, (3) mass conservation, and (4) a stable and good convergence rate. Based on this wall-boundary condition, if a solid wall is immersed in a fluid, then by applying Gauss's theorem, the formulas for computing the force and torque acting on the solid wall from fluid flow are derived from the volume integrals over the solid volume instead of from the surface integrals over the solid surface. Based on the pressure-based LBM, inlet and outlet boundary conditions are also proposed. The order of accuracy of the proposed boundary condition is demonstrated with the errors of the velocity field, wall stress, and gradients of velocity and pressure. The steady flow past a circular cylinder is simulated to demonstrate the efficiency and capabilities of the proposed unified method.

UR - http://www.scopus.com/inward/record.url?scp=84961317486&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961317486&partnerID=8YFLogxK

U2 - 10.1017/jmech.2014.80

DO - 10.1017/jmech.2014.80

M3 - Article

VL - 31

SP - 55

EP - 68

JO - Journal of Mechanics

JF - Journal of Mechanics

SN - 1727-7191

IS - 1

ER -