Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials.
Universidade Federal do Rio de Janeiro, 68.528, Rio de Janeiro, RJ 21941-972, Brazil.
Rodrigo C V
RC
Coelho
Instituto Nacional de Metrologia, Normalização e Qualidade Industrial, Duque de Caxias, RJ 25.250-020, Brazil.
Anderson
A
Ilha
Universidade Federal do Rio de Janeiro, 68.528, Rio de Janeiro, RJ 21941-972, Brazil.
Mauro M
MM
Doria
Instituto Nacional de Metrologia, Normalização e Qualidade Industrial, Duque de Caxias, RJ 25.250-020, Brazil.
R M
RM
Pereira
Instituto Nacional de Metrologia, Normalização e Qualidade Industrial, Duque de Caxias, RJ 25.250-020, Brazil.
Valter Yoshihiko
VY
Aibe