A lattice Boltzmann method based on generalized polynomials and its application for electrons in metals

TL;DR

This paper introduces a novel lattice Boltzmann method utilizing generalized orthonormal polynomials, enabling accurate simulation of semi-classical fluids like electrons in metals, validated through the Riemann problem.

Contribution

It develops a new lattice Boltzmann approach based on generalized polynomials, extending the Hermite polynomial framework for semi-classical fluid modeling.

Findings

The method accurately models electrons in metals.

Validation performed using the Riemann problem.

Generalized polynomials improve flexibility over traditional Hermite polynomials.

Abstract

A lattice Boltzmann method is proposed based on the expansion of the equilibrium distribution function in powers of a new set of generalized orthonormal polynomials which are here presented. The new polynomials are orthonormal under the weight defined by the equilibrium distribution function itself. The D-dimensional Hermite polynomials is a sub-case of the present ones, associated to the particular weight of a gaussian function. The proposed lattice Boltzmann method allows for the treatment of semi-classical fluids, such as electrons in metals under the Drude-Sommerfeld model, which is a particular case that we develop and validate by the Riemann problem.