High-order upwind compact finite-difference lattice Boltzmann method for viscous incompressible flows

Abstract

In this work, a high-order upwind compact finite-difference lattice Boltzmann method (UCDLBM) is developed to efficiently solve viscous incompressible flow problems. A fifth-order upwind compact difference scheme is adopted to discretize the spatial derivatives of the lattice Boltzmann equation, and the third-order total-variation-diminishing Runge–Kutta scheme is utilized for the discretization of the temporal term. Compared to the existing central compact finite-difference lattice Boltzmann method (CFDLBM), the present UCDLBM can prevent non-physical oscillations without filtering due to the natural dissipative property of upwind schemes. Three benchmark problems involving the Taylor–Green vortex problem, the doubly periodic shear layer flow problem and the lid driven square cavity flow problem are numerically solved to demonstrate the accuracy and efficiency of the present method. Numerical results computed are in good agreement with the analytical solution or other available numerical results. And, the present UCDLBM is less time-consuming than the CFDLBM without degenerating the order of accuracy of the numerical solutions.