Two-dimensional thermal model of the finite-difference lattice Boltzmann method with high spatial isotropy

The existing lattice Boltzmann method multispeed thermal models show a limited accuracy. This paper proposes a two-dimensional multispeed thermal model for the finite-difference lattice Boltzmann method (FDLBM). To recover correct fluid equations, up to fourth orders of local flow velocity should be retained in the local equilibrium distribution function and tensors of particle velocities should have up to seventh rank isotropy. In the FDLBM, particle velocities can be selected independently from the lattice configuration. Therefore, particle velocities of octagonal directions, which have up to seventh rank isotropic tensors, are adopted. The proposed model was verified by two simulations. The model showed excellent numerical stability in addition to strict accuracy.