Development of a Fourier-expansion based differential quadrature method with lattice Boltzmann flux solvers: Application to incompressible isothermal and thermal flows

This paper presents a high-order Fourier-expansion based differential quadrature method with isothermal and thermal lattice Boltzmann flux solvers (LBFS-FDQ and TLBFS-FDQ) for simulating incompressible flows. The numerical solution in the present method is approximated via trigonometric basis. Therefore, both periodic and non-periodic boundary conditions can be handled straightforwardly without the special treatments as required by polynomial-based differential quadrature methods. The incorporation of LBFS/TLBFS enables the present methods to efficiently simulated various types of flow problems on considerably coarse grids with spectral accuracy. The high-order accuracy, efficiency and competitiveness of the proposed method are comprehensively demonstrated through a wide selection of isothermal and thermal flow benchmarks.