Computation of three-dimensional incompressible flows using high-order weighted essentially non-oscillatory finite-difference lattice Boltzmann method

Abstract

In the present work, an accurate and robust solution methodology based on the high-order weighted essentially non-oscillatory (WENO) finite-difference lattice Boltzmann method (LBM) in the three-dimensional generalized curvilinear coordinates is presented and applied for simulating the three-dimensional incompressible flows over complicated configurations with curved boundaries. Here, the incompressible form of the lattice Boltzmann equation in three dimensions is considered and the discretization of the spatial derivative terms is performed with the fifth-order WENO finite-difference method and the temporal derivative term is discretized with the fourth-order Runge–Kutta scheme to ensure the accuracy and stability of the solution method for both the steady and unsteady problems. The three-dimensional lattice Boltzmann equation applied here is based on a nineteen discrete velocity model for transforming the microscopic properties to the macroscopic ones. To assess the accuracy and robustness of the present three-dimensional high-order finite-difference LBM solver, different incompressible flow benchmarks and practical test cases are studied that are the cavity flow, the Beltrami flow, the flow in the curved ducts of rectangular cross sections, and the flow over a sphere for different flow conditions. The decay of the homogeneous isotropic turbulence is also computed to examine the suitability of the present solution method to be applied as the direct numerical simulation of turbulent flows. It is demonstrated that the solution methodology presented based on the high-order WENO finite-difference LBM in the three-dimensional generalized curvilinear coordinate can be used for accurately and effectively computing the three-dimensional practical incompressible flow problems.