Galilean invariance study on different lattice Boltzmann fluid–solid interface approaches for vortex-induced vibrations

The theory of the lattice Boltzmann automaton is based on a moment transform which is not Galilean invariant. It is explained how the central moments transform, used in the cascaded lattice Boltzmann method, overcomes this problem by choosing the center of mass coordinate system as the frame of reference. Galilean invariance is restored and the form of the kinetic theory is unaffected. Conservation laws are not compromised by the high order polyinomials in the equilibrium distribution arising from the central moment transform. Two sources of instabilities in lattice Boltzmann simulations are discussed: negative numerical viscosity due to insufficient Galilean invariance and aliasing. The cascaded lattice Boltzmann automaton overcomes both problems. It is discussed why aliasing is unavoidable in lattice Boltzmann methods that rely on a single relaxation time. An appendix lists the complete scattering operator of the D2Q9 cascaded lattice Boltzmann automaton.

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Investigation of Galilean invariance of multi-phase lattice Boltzmann methods

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2005.09.030 ◽

2006 ◽

Vol 362 (1) ◽

pp. 105-110 ◽

Cited By ~ 25

Author(s):

A.J. Wagner ◽

Q. Li

Keyword(s):

Lattice Boltzmann ◽

Galilean Invariance ◽

Lattice Boltzmann Methods ◽

Multi Phase

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Thermodynamic consistency in deriving lattice Boltzmann models for describing segregation in non-ideal mixtures

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2011.0021 ◽

2011 ◽

Vol 369 (1944) ◽

pp. 2292-2300 ◽

Cited By ~ 5

Author(s):

Paulo Cesar Philippi ◽

Luis Orlando Emerich Dos Santos ◽

Luiz Adolfo Hegele ◽

Carlos Enrique Pico Ortiz ◽

Diogo Nardelli Siebert ◽

...

Keyword(s):

Kinetic Model ◽

Lattice Boltzmann ◽

Thermodynamic Consistency ◽

Galilean Invariance ◽

Moment Equations ◽

Invariance Condition ◽

Boltzmann Equations ◽

Lattice Boltzmann Models ◽

First Moment ◽

Lattice Boltzmann Equations

The thermodynamic consistency of kinetic models for non-ideal mixtures in non-isothermal conditions is investigated. A kinetic model is proposed that is suitable for deriving high-order lattice Boltzmann equations by an appropriate discretization of the velocity space, satisfying the Galilean invariance condition and free of spurious terms in the first moment equations.

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Dependence of drag on a Galilean invariance-breaking parameter in lattice Boltzmann flow simulations

Physical Review E ◽

10.1103/physreve.49.2115 ◽

1994 ◽

Vol 49 (3) ◽

pp. 2115-2118 ◽

Cited By ~ 6

Author(s):

Lukas Wagner

Keyword(s):

Lattice Boltzmann ◽

Galilean Invariance ◽

Flow Simulations ◽

Breaking Parameter

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Lattice Boltzmann method: simulation of isothermal low-speed flows

Keldysh Institute Preprints ◽

10.20948/prepr-2021-99 ◽

2021 ◽

pp. 1-31

Author(s):

Georgy Sergeevich Chashchin

Keyword(s):

Fluid Dynamics ◽

Kinetic Theory ◽

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Computational Algorithm ◽

Hermite Polynomials ◽

Modern Method ◽

Theoretical Background ◽

Galilean Invariance ◽

Boltzmann Method

In this work, lattice Boltzmann method on standard lattices was descript as one of the modern method of computation fluid dynamics. The article has main theorems, which prove computational algorithm, different type’s boundary conditions and defect in Galilean invariance. Moreover, the paper has some theoretical background about physical kinetic theory, Hermite polynomials and numeric integration. Here has not any new scientist discoveries, but has explanation of basic lattice Boltzmann theory.

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