Renormalization of the lattice Boltzmann hierarchy

2007/03/16 by I. V. Karlin, Iliya V. Karlin, Santosh Ansumali +1
Engineering · Mathematics · Physics and Astronomy · #Aerodynamics and Fluid Dynamics Research #Bhatnagar–Gross–Krook operator #Boltzmann equation #Classical mechanics #Couette flow #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #HPP model #Kinetic energy #Kinetic theory #Knudsen number #Lattice Boltzmann Simulation Studies #Lattice Boltzmann methods #Lattice gas automaton #Mathematical physics #Mathematics #Mechanics #Physics #Quantum mechanics #Renormalization #Statistical physics #Thermodynamics #cond-mat.stat-mech #physics.comp-ph #physics.flu-dyn

paper · pdf · doi:10.1103/physreve.76.025701

published as Phys. Rev. E 76, 025701(R) (2007) (4 pages) · 4 pages, 1 figure

arxiv created 2007/03/16 · openalex publication_date 2007/08/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Is it possible to solve Boltzmann-type kinetic equations using only a small number of particle velocities? We introduce a technique of solving kinetic equations with a (arbitrarily) large number of particle velocities using only a lattice Boltzmann method on standard, low-symmetry lattices. The renormalized kinetic equation is validated with an exact solution of the planar Couette flow at moderate Knudsen numbers.

Citations

• The renormalization group and the ε expansion
• Kinetic theory of turbulence modeling: smallness parameter, scaling and microscopic derivation of Smagorinsky model
• Lattice Boltzmann method for thermal flow simulation on standard lattices
• Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation
• Quasi-equilibrium lattice Boltzmann method
• Hydrodynamics beyond Navier-Stokes: Exact Solution to the Lattice Boltzmann Hierarchy