Variable property-based lattice Boltzmann flux solver for thermal flows in the low Mach number limit

Abstract

A variable property-based lattice Boltzmann flux solver (VPLBFS) is proposed in this paper for thermal flows with partial or total variation in fluid properties in the low Mach number limit. In the solver, one particle distribution function is introduced for pressure and momentum, and another for fluid temperature. The fluid properties are assumed to be functions of only the local fluid temperature. The macroscopic variables at cell centers are determined from the solution of macroscopic governing equations by the finite volume method. The fluxes at cell interfaces are evaluated by the local construction of the solution for the standard lattice Boltzmann equation. The additional terms due to fluid property variations and body forces are regarded as source terms and treated by the finite volume discretization. These features make its application on non-uniform grids with a fixed time interval more flexible in comparison with conventional lattice Boltzmann models. The VPLBFS is validated by several numerical examples, including fluid flows between two parallel plates, with one plate to be isothermally heated from a certain moment, the natural convection in a square cavity with a large temperature difference and the natural convection of supercritical carbon dioxide. Numerical results show the reliability of the VPLBFS for thermal flows with partial or total variation in fluid properties.