Renormalization of the Lattice Boltzmann Hierarchy

TL;DR

This paper introduces a new method to solve complex kinetic equations with many particle velocities using a simplified lattice Boltzmann approach on low-symmetry lattices, validated against exact solutions.

Contribution

It presents a novel renormalization technique enabling the use of fewer velocities in lattice Boltzmann simulations of kinetic equations.

Findings

Validated with exact solutions of planar Couette flow

Effective for moderate Knudsen numbers

Works on standard low-symmetry lattices

Abstract

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