Bulk and shear viscosities in lattice Boltzmann equations
P. J. Dellar (2001) Bulk
and shear viscosities in lattice Boltzmann equations Phys.
Rev. E 64 031203 (11 pages). DOI: 10.1103/PhysRevE.64.031203
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Abstract
Lattice Boltzmann equations (LBE) are a useful tool for simulating the
incompressible Navier-Stokes equations. However, LBE actually simulate
a compressible but usually isothermal fluid at some small but finite
Mach number. There has been recent interest in using LBE at larger, but
still subsonic, Mach numbers, for which the viscous terms in the resulting
momentum equation depart appreciably from those in the compressible Navier-Stokes
equations. In particular, the isothermal constraint implies a nonzero ``bulk''
viscosity in addition to the usual shear viscosity. This difficulty arises
at the level of the isothermal continuum Boltzmann equation prior
to discretization. A remedy is proposed, and tested in numerical experiments
with decaying sound waves. Conversely, an enhanced bulk viscosity is found
useful for identifying or suppressing artifacts in under-resolved simulations
of supposedly incompressible shear flows.
BibTeX citation information:
@article{Dellar01BulkVisc,
author = "P. J. Dellar",
year = "2001",
title = "Bulk and shear viscosities in lattice {Boltzmann} equations",
journal = "Phys. Rev. E",
volume = "64",
pages = "031203 (11 pages)",
URL = "http://link.aps.org/abstract/PRE/v64/e031203",
DOI = "10.1103/PhysRevE.64.031203"}
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