Volume 116, Number 2, October 2016
|Number of page(s)||6|
|Published online||28 November 2016|
A lattice Boltzmann method based on generalized polynomials and its application for electrons in metals
1 Departamento de Física dos Sólidos, Universidade Federal do Rio de Janeiro - 21941-972, Rio de Janeiro, Brazil
2 ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials Schafmattstrasse 6, HIF, CH-8093 Zürich, Switzerland
3 Instituto Nacional de Metrologia, Normalização e Qualidade Industrial - Duque de Caxias 25.250-020, RJ, Brazil
4 Dipartimento di Fisica, Università di Camerino - I-62032 Camerino, Italy
Received: 30 May 2016
Accepted: 9 November 2016
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.
PACS: 02.70.-c – Computational techniques; simulations / 05.10.-a – Computational methods in statistical physics and nonlinear dynamics / 47.11.Qr – Lattice gas
© EPLA, 2016
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