Implicitcorrectionbased immersed boundarylattice Boltzmann method with two relaxation times
Abstract
In the present paper, we verify the effectiveness of the tworelaxationtime (TRT) collision operator in reducing boundary slip computed by the immersed boundarylattice Boltzmann method (IBLBM). In the linear collision operator of the TRT, we decompose the distribution function into symmetric and antisymmetric components and define the relaxation parameters for each part. The ChapmanEnskog expansion indicates that one relaxation time for the symmetric component is related to the kinematic viscosity. Rigorous analysis of the symmetric shear flows reveals that the relaxation time for the antisymmetric part controls the velocity gradient, the boundary velocity, and the boundary slip velocity computed by the IBLBM. Simulation of the symmetric shear flows, the symmetric Poiseuille flows, and the cylindrical Couette flows indicates that the profiles of the numerical velocity calculated by the TRT collision operator under the IBLBM framework exactly agree with those of the multirelaxation time (MRT). The TRT is as effective in removing the boundary slip as the MRT. We demonstrate analytically and numerically that the error of the boundary velocity is caused by the smoothing technique using the δ function used in the interpolation method. In the simulation of the flow past a circular cylinder, the IBLBM based on the implicit correction method with the TRT succeeds in preventing the flow penetration through the solid surface as well as unphysical velocity distortion. The drag coefficient, the wake length, and the separation points calculated by the present IBLBM agree well with previous studies at Re = 10, 20, and 40.
 Publication:

Physical Review E
 Pub Date:
 February 2014
 DOI:
 10.1103/PhysRevE.89.023307
 Bibcode:
 2014PhRvE..89b3307S
 Keywords:

 47.11.j;
 02.60.Lj;
 83.50.Rp;
 Computational methods in fluid dynamics;
 Ordinary and partial differential equations;
 boundary value problems;
 Wall slip and apparent slip