Thermal lattice Boltzmann flux solver and its application for simulation of incompressible thermal flows

• It is first time to present thermal lattice Boltzmann flux solver for thermal flows.
• Fluxes are evaluated from local reconstruction of lattice Boltzmann solution.
• Combine advantages of conventional Navier–Stokes and lattice Boltzmann solvers.
• Overcome disadvantages of standard lattice Boltzmann solver.

A thermal lattice Boltzmann flux solver (TLBFS) is developed in this work for simulation of incompressible thermal flows. In TLBFS, the thermal lattice Boltzmann method (TLBM) is only applied to reconstruct the local solution of TLBM for evaluation of fluxes at the cell interface. Meanwhile, the macroscopic flow variables at cell centers are obtained by using the finite volume method to solve conservative differential equations recovered from Chapman–Enskog analysis of thermal lattice Boltzmann equation. The physical boundary conditions in TLBFS can be directly implemented using the same way as in conventional Navier–Stokes (N–S) solvers. The present solver eliminates the constraints associated with conventional lattice Boltzmann method such as limitation to uniform Cartesian mesh, tie-up between the time step and the mesh spacing, as well as implementation of boundary conditions for distribution functions. TLBFS is validated through numerical examples of natural convection in enclosures, including a square cavity and a cylindrical annulus, and mixed convection from a heated cylinder. Through numerical validation, it is shown that TLBFS can be effectively and flexibly applied to solve thermal flow problems with curved boundaries.