A lattice-Boltzmann method with hierarchically refined meshes

A lattice-Boltzmann method (LBM) with local hierarchical adaptive grid refinement using a cell-centered lattice structure is presented which satisfies the requirements of high accuracy and high efficiency. It is applied to two-dimensional and three-dimensional laminar and turbulent flows over cylinders and spheres which constitute a comprehensive validation of LB methods for such blunt body problems. In the turbulent flow regime, a large-eddy simulation is used to capture the flow physics up to the inertial subrange. The numerical approach is described in detail and the accuracy of the method is demonstrated by considering the flow around a circular cylinder at Reynolds numbers Re = 20, 40, and 100 and the flow past a sphere at Re = 100, 300, 3700, and 10,000. The LBM plus local hierarchical grid refinement yields accurate temporal and spatial results and dramatically increases the computational efficiency by globally reducing the number of cells.

► A LBM with local hierarchical adaptive grid refinement is presented.
► The techniques for interpolation and subgrid-scale modeling are described in detail.
► The method is applied to two- and three-dimensional laminar and turbulent flows.
► Accurate results are obtained while the computational efficiency is greatly improved.