A high-order generalized differential quadrature method with lattice Boltzmann flux solver for simulating incompressible flows

Abstract

This paper presents a high-order generalized differential quadrature method with lattice Boltzmann flux solver (LBFS-GDQ) for simulating incompressible isothermal flows. In this method, high-order polynomials are adopted to approximate both the solution and fluxes globally across the computational domain. Solution derivatives and flux divergence are conveniently computed by the GDQ method. At the interior solution points, the viscous and inviscid fluxes are evaluated simultaneously via LBFS. Treatments to prevent the global accuracy from being contaminated by the streaming error of LBFS are proposed and studied, including the choice for the local streaming spacing and interpolation methods for the local reconstruction. The present method inherits the advantages of both GDQ and LBFS, i.e., global spectral accuracy, direct evolution of macroscopic variables, and convenient implementation of boundary conditions. Numerical experiments with a wide selection of incompressible flow problems confirm the excellent accuracy, efficiency, and flexibility of the proposed method.