Improved bounce-back methods for no-slip walls in lattice-Boltzmann schemes: Theory and simulations

M Rohde, D Kandhai, JJ Derksen, HEA Van den Akker

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

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 is first-order accurate in space, and the method of Bouzidi 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.

Original languageEnglish
Article number066703
Number of pages10
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume67
Issue number6
DOIs
Publication statusPublished - Jun 2003

Keywords

  • BOUNDARY-CONDITIONS
  • FLUID
  • ACCURACY
  • DYNAMICS
  • FLOWS
  • BGK

Cite this

Improved bounce-back methods for no-slip walls in lattice-Boltzmann schemes : Theory and simulations. / Rohde, M; Kandhai, D; Derksen, JJ; Van den Akker, HEA.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 67, No. 6, 066703, 06.2003.

Research output: Contribution to journalArticle

@article{45c122a3fc28439584affd34a994fdde,
title = "Improved bounce-back methods for no-slip walls in lattice-Boltzmann schemes: Theory and simulations",
abstract = "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 is first-order accurate in space, and the method of Bouzidi 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.",
keywords = "BOUNDARY-CONDITIONS, FLUID, ACCURACY, DYNAMICS, FLOWS, BGK",
author = "M Rohde and D Kandhai and JJ Derksen and {Van den Akker}, HEA",
year = "2003",
month = "6",
doi = "10.1103/PhysRevE.67.066703",
language = "English",
volume = "67",
journal = "Physical Review. E, Statistical, Nonlinear and Soft Matter Physics",
issn = "1539-3755",
publisher = "AMER PHYSICAL SOC",
number = "6",

}

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, JJ

AU - Van den Akker, HEA

PY - 2003/6

Y1 - 2003/6

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 is first-order accurate in space, and the method of Bouzidi 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 is first-order accurate in space, and the method of Bouzidi 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.

KW - BOUNDARY-CONDITIONS

KW - FLUID

KW - ACCURACY

KW - DYNAMICS

KW - FLOWS

KW - BGK

U2 - 10.1103/PhysRevE.67.066703

DO - 10.1103/PhysRevE.67.066703

M3 - Article

VL - 67

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 6

M1 - 066703

ER -