TY - JOUR

T1 - Improved bounce-back methods for no-slip walls in lattice-Boltzmann schemes

T2 - Theory and simulations

AU - Rohde, M.

AU - Kandhai, D.

AU - Derksen, J. J.

AU - Van den Akker, H. E.A.

PY - 2003

Y1 - 2003

N2 - A detailed analysis is presented for the accuracy of several bounce-back methods for imposing no-slip walls in lattice-Boltzmann schemes. By solving the lattice-BGK (Bhatnagar-Gross-Krook) equations analytically in the case of plane Poiseuille flow, it is found that the volumetric approach by Chen et al. is first-order accurate in space, and the method of Bouzidi et al. second-order accurate in space. The latter method, however, is not mass conservative because of errors associated with interpolation of densities residing on grid nodes. Therefore, similar interpolations are applied to Chen’s volumetric scheme, which indeed improves the accuracy in the case of plane Poiseuille flow with boundaries parallel to the underlying grid. For skew boundaries, however, it is found that the accuracy remains first order. An alternative volumetric approach is proposed with a more accurate description of the geometrical surface. This scheme is demonstrated to be second-order accurate, even in the case of skew channels. The scheme is mass conservative in the propagation step because of its volumetric description, but still not in the collision step. However, the deviation in the mass is, in general, found to be small and proportional to the second-order terms in the standard BGK equilibrium distribution. Consequently, the scheme is a priori mass conservative for Stokes flow.

AB - A detailed analysis is presented for the accuracy of several bounce-back methods for imposing no-slip walls in lattice-Boltzmann schemes. By solving the lattice-BGK (Bhatnagar-Gross-Krook) equations analytically in the case of plane Poiseuille flow, it is found that the volumetric approach by Chen et al. is first-order accurate in space, and the method of Bouzidi et al. second-order accurate in space. The latter method, however, is not mass conservative because of errors associated with interpolation of densities residing on grid nodes. Therefore, similar interpolations are applied to Chen’s volumetric scheme, which indeed improves the accuracy in the case of plane Poiseuille flow with boundaries parallel to the underlying grid. For skew boundaries, however, it is found that the accuracy remains first order. An alternative volumetric approach is proposed with a more accurate description of the geometrical surface. This scheme is demonstrated to be second-order accurate, even in the case of skew channels. The scheme is mass conservative in the propagation step because of its volumetric description, but still not in the collision step. However, the deviation in the mass is, in general, found to be small and proportional to the second-order terms in the standard BGK equilibrium distribution. Consequently, the scheme is a priori mass conservative for Stokes flow.

UR - http://www.scopus.com/inward/record.url?scp=84907832631&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.67.066703

DO - 10.1103/PhysRevE.67.066703

M3 - Article

AN - SCOPUS:84907832631

SN - 1063-651X

VL - 67

SP - 10

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 6

ER -