A generic, mass conservative local grid refinement technique for lattice‐Boltzmann schemes

Abstract

AbstractA generic, mass conservative local grid refinement technique for the lattice‐Boltzmann method (LBM) is proposed. As a volumetric description of the lattice‐Boltzmann equation is applied, mass conservation can be imposed by allowing the lattice‐Boltzmann particles to move from coarse grid cells to fine grid cells and vice versa in the propagation step. In contrast to most existing techniques, no spatial and temporal interpolation of particle densities is applied. Moreover, since the communication between the coarse and the fine grids is independent on the collision step, the method can be used for any LBM scheme.It was found that the method is second‐order accurate in space for 2‐D Poiseuille flow and different grid setups. The method was also applied to the case of 2‐D lid driven cavity flow at Re=1000, where half of the cavity was locally refined. It was found that the locations of the two lower vortices could be captured accurately. Finally, a direct numerical simulation (DNS) of turbulent channel flow at Reτ=360 was performed where the grid was locally refined near the walls of the channel. Good first‐ and second‐order turbulence statistics were obtained, showing the applicability of the local grid refinement technique for complex flows. Copyright © 2005 John Wiley & Sons, Ltd.