Implementation of the force term in half-range lattice Boltzmann models

Abstract

In the frame of the Boltzmann equation, wall-bounded flows of rarefied gases require the implementation of boundary conditions at the kinetic level. Such boundary conditions induce a discontinuity in the distribution function with respect to the component of the momentum which is normal to the boundary. Expanding the distribution function with respect to half-range polynomials allows this discontinuity to be captured. The implementation of this concept has been reported in the literature only for force-free flows. In the case of general forces which can have non-zero components in the direction perpendicular to the walls, the implementation of the force term requires taking the momentum space gradient of a discontinuous function. Our proposed method deals with this difficulty by employing the theory of distributions. We validate our procedure by considering the simple one-dimensional flow between diffuse-reflective walls of equal or different temperatures driven by the constant gravitational force. For this flow, a comparison between the results obtained with the full-range and the half-range Gauss-Hermite LB models is also presented.

arXiv comment55 pages, 9 figures, 2 tables

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Cited by in corpus (2)

• High-order quadrature-based lattice Boltzmann models for the flow of ultrarelativistic rarefied gases
• Lattice Boltzmann models based on the vielbein formalism for the simulation of flows in curvilinear geometries