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. A Fourier-expansion based differential quadrature method (FDQ) with lattice Boltzmann flux solvers (LBFS) for simulating isothermal and thermal flows. The method possesses several merits such as simple formulation and implementation, easy boundary condition treatments and flexibility on curved geometries. Numerical experiments confirm the superior performance in terms of accuracy and efficiency compared with other high-order methods. image