Improved bounce-back methods for no-slip walls in lattice-Boltzmann schemes: Theory and simulations. Rohde, M., Kandhai, D., Derksen, J., J., & Van den Akker, H., E. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 67(6):10, 2003.
Improved bounce-back methods for no-slip walls in lattice-Boltzmann schemes: Theory and simulations [link]Website  abstract   bibtex   
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.
@article{
 title = {Improved bounce-back methods for no-slip walls in lattice-Boltzmann schemes: Theory and simulations},
 type = {article},
 year = {2003},
 identifiers = {[object Object]},
 pages = {10},
 volume = {67},
 websites = {https://www.ncbi.nlm.nih.gov/pubmed/16241376},
 city = {Kramers Laboratorium voor Fysische Technologie, Delft University of Technology, Delft, The Netherlands. m.rhode@klft.tn.tudelft.nl},
 edition = {2005/10/26},
 id = {49877871-e845-367c-966a-f190dcb9029f},
 created = {2018-06-29T18:31:09.271Z},
 file_attached = {false},
 profile_id = {51877d5d-d7d5-3ec1-b62b-06c7d65c8430},
 group_id = {efaa6fc9-0da5-35aa-804a-48d291a7043f},
 last_modified = {2018-10-02T09:30:06.366Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Rohde2003},
 source_type = {JOUR},
 notes = {Rohde, M<br/>Kandhai, D<br/>Derksen, J J<br/>Van den Akker, H E A<br/>eng<br/>Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jun;67(6 Pt 2):066703. doi: 10.1103/PhysRevE.67.066703. Epub 2003 Jun 10.},
 private_publication = {false},
 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 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.},
 bibtype = {article},
 author = {Rohde, M. and Kandhai, D. and Derksen, J. J. and Van den Akker, H. E.A.},
 journal = {Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
 number = {6}
}

Downloads: 0