Preconditioned WENO finite-difference lattice Boltzmann method for simulation of incompressible turbulent flows

Abstract

In this work, a preconditioned high-order weighted essentially non-oscillatory (WENO) finite-difference lattice Boltzmann method (WENO-LBM) is applied to deal with the incompressible turbulent flows. Two different turbulence models namely, the Spalart–Allmaras (SA) and k−ωSST models are used and applied in the solution method for this aim. The spatial derivatives of the two-dimensional (2D) preconditioned LB equation in the generalized curvilinear coordinates are discretized by using the fifth-order WENO finite-difference scheme and an implicit–explicit Runge–Kutta scheme is adopted for the time discretization. For the convective and diffusive terms of the turbulence transport equations, the third-order WENO and second-order central finite-difference schemes are used, respectively. The preconditioning technique along with the local time-stepping method are applied to the WENO-LBM to further accelerate the solution to the converged steady-state condition, and therefore, an accurate and efficient incompressible LB solver is provided for simulating turbulent flows. The accuracy and robustness of the proposed solution method are assessed by computing two test cases: the 2D turbulent flow over a flat plate at Re=1.0×107 and the 2D turbulent flow over a NACA0012 airfoil at Re=6.0×106 and different angles of attack. The present results are compared with the available numerical and experimental results which show excellent agreement. It is demonstrated that the present solution methodology based on the WENO-LBM provides more accurate results of the incompressible turbulent flows and it requires lower number of grid points compared to the traditional (low-order accurate) LB and Navier–Stokes solvers.