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arXiv · 1510.07328

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

Rodrigo C. V. Coelho·Anderson Ilha·Mauro M. Doria
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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.

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Rodrigo C. V. Coelho, Anderson Ilha, Mauro M. Doria. 2017-03-12. A lattice Boltzmann method based on generalized polynomials and its application for electrons in metals. https://doi.org/10.1209/0295-5075%2F116%2F20001

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