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

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.

6 pages, 3 figures

References in corpus (3)

• Consistent Lattice Boltzmann Method
• Relativistic Lattice Boltzmann Model with Improved Dissipation
• Lattice Boltzmann method for bosons and fermions and the fourth order Hermite polynomial expansion

Cited by in corpus (5)

• Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene
• Lattice Boltzmann method for semiclassical fluids
• Fully dissipative relativistic lattice Boltzmann method in two dimensions
• Lattice Wigner equation
• Chebyshev, Legendre, Hermite and other orthonormal polynomials in D-dimensions