Duality in matrix lattice Boltzmann models

2007/11/30 by Rajat Adhikari, R. Adhikari, Sauro Succi +1 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Aerosol Filtration and Electrostatic Precipitation #Bhatnagar–Gross–Krook operator #Boltzmann equation #Classical mechanics #Duality (order theory) #Fluid Dynamics and Turbulent Flows #HPP model #Kinetic energy #Lattice (music) #Lattice Boltzmann Simulation Studies #Lattice Boltzmann methods #Materials science #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Pure mathematics #Quantum mechanics #Statistical physics #Thermodynamics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.78.066701

12 pages, 3 figures

arxiv created 2007/11/30 · openalex publication_date 2008/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The notion of duality between the hydrodynamic and kinetic (ghost) variables of lattice kinetic formulations of the Boltzmann equation is introduced. It is suggested that this notion can serve as a guideline in the design of matrix versions of the lattice Boltzmann equation in a physically transparent and computationally efficient way.

Citations

• Lattice BGK Models for Navier-Stokes Equation
• Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation
• Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability
• Fluctuating lattice Boltzmann
• LATTICE BOLTZMANN METHOD FOR FLUID FLOWS

Cited by

• Generalized lattice Boltzmann method: Modeling, analysis, and elements
• Multiple-relaxation-time lattice Boltzmann approach to compressible flows with flexible specific-heat ratio and Prandtl number

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• Derivation of Hydrodynamics for Multi-Relaxation Time Lattice Boltzmann using the Moment-Approach