Higher-order non-linear scheme of finite-difference lattice Boltzmann method (Evaluation by direct numerical simulation of turbulent channel flow)

The resolution and efficiency of the finite-difference lattice Boltzmann method (FDLBM) is improved to deal with wall-bounded turbulence, which is characterized by the strong shear and anisotropy. FDLBM puts the merit of LBM, which is the explicit and non-iterative algorithm, into practice on the body-fitted coordinate in the conventional solvers based on Navier-Stokes equation of motion. Thus the performance of FDLBM is mostly affected by the finite-difference scheme for the advection terms of LBM, which has to be an upwind one from a stand point of numerical stability. Particularly in this study, the influences of the the order of accuracy and upwind method are assessed by the direct numerical simulation of fully-developed turbulent flow in a plane channel. We introduce a discretization method with numerical flux similar to the finite-volume method, and a nonlinear scheme which localizes the effect of the numerical diffusion. Our method successfully reproduced the mean velocity and turbulence statistics in comparison with standard database. We confirmed that the nonlinear scheme improved the resolution. Increase of reproducibility with the higher order scheme surpassed increment of its computational cost. The 7th-order scheme, for example, provided a comparable result to that by the 3rd-order scheme using 4 times finer grid, though the calculation time increases just 20 % at the same resolution. This higher-order nonlinear scheme proposed in this study, by reducing the requirement of computational resources, can extend the applicability of LBM for DNS and LES of turbulent flows.