High-order simplified thermal lattice Boltzmann method for incompressible thermal flows

Abstract

A high-order simplified thermal lattice Boltzmann method (HSTLBM) is developed in this paper for accurate and efficient simulation of incompressible thermal flows. The derivation of HSTLBM stems from the recently developed simplified thermal lattice Boltzmann method (STLBM) and incorporates high-order interpolation algorithms, which reflects an effective combination of local second-order reconstruction and global high-order scheme. By introducing virtual streaming nodes, HSTLBM decouples the streaming distance from the mesh spacing and then correlates them through high-order interpolation scheme. Delicate parametric studies indicate that adopting 5-point Lagrange interpolation and setting the streaming distance as 0.2 times of the mesh spacing could give optimal results which balances computational accuracy, stability, and efficiency well; and third-order of global accuracy can be achieved. HSTLBM inherits various merits of STLBM, especially its nice numerical stability. As a result, HSTLBM can give accurate and stable solutions on coarser meshes for problems at high Reynolds/Rayleigh numbers. Higher efficiency and lower memory cost can thus be expected. A series of benchmark tests are provided for comprehensive evaluation of HSTLBM in modelling two- and three-dimensional problems and on uniform/non-uniform meshes.