Stability of lattice Boltzmann methods in hydrodynamic regimes

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

Volumn 56, Issue 2, 1997, Pages 2243-2253

  Worthing, Rodney A ^a   Mozer, Joel ^a   Seeley, Guy ^a  

^a AIR FORCE RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000497337     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.2243     Document Type: Article

References (20)

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7. It would be correct to say that the scale at which the desired partial differential equation is approached is vastly different for the two methods, but no formal theory addressing this disparity has been put forth in the literature.
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11. This is a general representation for fully complex (Formula presented). One may want to restrict the stability analysis to allow for only real (Formula presented). This issue may be particularly important at the highest frequencies, (Formula presented) and (Formula presented). However, ignore this point for the moment.
12. By “highest” we mean those not representable on the given lattice. In general these frequencies will be aliased back upon those that are representable; however, this projection is assumed small and neglected in this work.
13. But computationally other instabilities that vary in space and time may occur and are considered later in this section.
14. Note that if one is treating a hexagonal mesh by subsuming it within a larger rectangular mesh (as we have done here), then this will put additional restrictions on the allowable wave numbers.
15. Doubled, since we wanted to preserve the superset argument.
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19. A potentially large space including free model parameters, mesh type and size, indicators of background flow amplitude and gradients, etc.
20. The value of the viscosity at (Formula presented) is taken from the accepted LB9 conversion (Formula presented).