Development of a high-order generalized differential quadrature element method with thermal lattice Boltzmann flux solver for simulation of incompressible thermal flows

This paper presents a high-order generalized differential quadrature element (GDQE)-thermal lattice Boltzmann flux solver (TLBFS) for simulating incompressible thermal flows. The GDQE method partitions the computational domain into multiple elements, within which the GDQ technique is applied to approximate solution gradients and flux divergences via high-order polynomial interpolations. The TLBFS is then utilized to reconstruct the distribution functions of density and internal energy, enabling the simultaneous evaluation of inviscid and viscous fluxes. Numerical examples confirm that the present method is well-suited for handling thermal flow problems with curved boundaries and complex geometry on arbitrary meshes, while achieving good solution accuracy and computational efficiency. The good performance also suggests the great potential in solving practical thermal flow problems.