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A Unified Wall-Boundary Condition for the Lattice Boltzmann Method and its Application to Force Evaluation

Published online by Cambridge University Press:  01 December 2014

S.-Y. Lin ,
Y.-H. Chin ,
F.-L. Yang ,
J.-F. Lin ,
J.-J. Hu ,
C.-S. Chen  and
S.-H. Hsieh
S.-Y. Lin
Affiliation:
Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan
Y.-H. Chin
Affiliation:
Marketing & Supply Chain Management, Overseas Chinese University Taichung, Taiwan
F.-L. Yang
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan
J.-F. Lin*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan
J.-J. Hu
Affiliation:
Department of Information Management, Shu-Te University Kaohsiung, Taiwan
C.-S. Chen
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan
S.-H. Hsieh
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan
*
* Corresponding author ([email protected]
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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.

Keywords

Unified wall-boundary conditionPressure-based lattice Boltzmann methodDirect forcing immersed boundary method
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 1 , February 2015 , pp. 55 - 68
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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