PMID: 11909246Mar 23, 2002Paper

Nonhydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
P J Dellar

Abstract

Lattice Boltzmann equations for the isothermal Navier-Stokes equations have been constructed systematically using a truncated moment expansion of the equilibrium distribution function from continuum kinetic theory. Applied to the shallow water equations, with its different equation of state, the same approach yields discrete equilibria that are subject to a grid scale computational instability. Different and stable equilibria were previously constructed by Salmon [J. Marine Res. 57, 503 (1999)]. The two sets of equilibria differ through a nonhydrodynamic or "ghost" mode that has no direct effect on the hydrodynamic behavior derived in the slowly varying limit. However, Salmon's equilibria eliminate a coupling between hydrodynamic and ghost modes, one that leads to instability with a growth rate increasing with wave number. Previous work has usually assumed that truncated moment expansions lead to stable schemes. Such instabilities have implications for lattice Boltzmann equations that simulate other nonideal equations of state, or that simulate fully compressible, nonisothermal fluids using additional particles.

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Oct 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P J Dellar

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Citations

Jul 2, 2010·Chaos·Jianying Zhang, Guangwu Yan
Feb 17, 2011·The Journal of Chemical Physics·Santtu T T OllilaTapio Ala-Nissila
Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Robert Rubinstein, Li-Shi Luo
Sep 17, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jian Guo Zhou, Haifei Liu
Aug 15, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Erlend Magnus Viggen
Jun 23, 2020·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·C CoreixasJ Latt
Sep 15, 2016·Physical Review. E·Liangqi ZhangJia Wei Chew
Apr 3, 2019·Physical Review. E·Rongzong HuangNikolaus A Adams
Jul 25, 2019·Physical Review. E·S A HosseiniD Thévenin
May 20, 2020·Physical Review. E·Gauthier WissocqPierre Sagaut
Oct 24, 2019·Physical Review. E·S ZitzJ Harting
Dec 18, 2020·Physical Review. E·Gauthier WissocqJean-François Boussuge
Apr 3, 2012·Physical Review Letters·L BiferaleF Toschi
Oct 2, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jianying ZhangXiubo Shi
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R Adhikari, S Succi

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