High-order least-square-based finite-difference-finite-volume method for simulation of incompressible thermal flows on arbitrary grids.

In this work, a high-order (HO) least-square-based finite difference-finite volume (LSFD-FV) method together with thermal lattice Boltzmann flux solver (TLBFS) is presented for simulation of two-dimensional (2D) incompressible thermal flows on arbitrary grids. In the present method, a HO polynomial based on Taylor series expansion is applied within each control cell, where the unknown spatial derivatives at each cell center are approximated by least-square-based finite difference (LSFD) scheme. Then the recently developed TLBFS is applied to evaluate the convective and diffusive fluxes simultaneously at the cell interface by local reconstruction of thermal lattice Boltzmann solutions of the density and internal energy distribution functions. The present HO LSFD-FV method is verified and validated by 2D incompressible heat transfer problems. Numerical results indicate that the present method can be effectively and flexibly applied to solve thermal flow problems with curved boundaries on arbitrary grids. Compared with the conventional low-order finite volume method, higher efficiency and lower memory cost make the present HO method more promising for practical thermal flow problems.