A wall function approach in lattice Boltzmann method: algorithm and validation using turbulent channel flow
Mengtao Han, Ryozo Ooka, Hideki Kikumoto
Abstract
Abstract In the lattice Boltzmann method (LBM), the widely utilized wall boundary is the bounce-back (BB) boundary, corresponding to the no-slip boundary. The BB boundary prevents the LBM from capturing the accurate shear drag on the wall when addressing high Reynolds number flows using coarse-grid systems. This study proposed the ‘wall-function bounce (WFB)’ boundary, a general framework to incorporate wall functions into the LBM’s boundary condition, independent of specific information of discrete velocity schemes and collision functions. The WFB boundary calculates the appropriate shear drag on the wall using a wall function model, and thereafter just modifies partial diagonal distribution functions to reflect the shear drag. The Spalding’s law was utilized as the wall function in WFB. Simulations of turbulent channel flow at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>R</mml:mtext> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>e</mml:mtext> </mml:mrow> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>640</mml:mn> <mml:mrow> <mml:mtext> and</mml:mtext> </mml:mrow> <mml:mrow/> <mml:mn>2003</mml:mn> </mml:math> using the LBM-based large-eddy simulation were conducted to validate the effectiveness of the proposed boundary condition. The results indicate that the BB boundary underestimated the time-averaged velocity in the buffer layer at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>R</mml:mtext> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>e</mml:mtext> </mml:mrow> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>640</mml:mn> </mml:math> , and the averaged velocity in the entire domain at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>R</mml:mtext> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>e</mml:mtext> </mml:mrow> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>2003</mml:mn> </mml:math> , when using coarse-grid systems. However, WFB obtained the proper shear drag on the wall and thus, compensated for the underestimation and agreed better with the experimental or direct numerical simulation data, especially at the 1st-layer grid. In addition, WFB improved the Reynolds normal stress in the near-wall region to some extent. The distributions of shear stress on the wall by WFB were analogous to those by the wall model function in the finite volume method.