Lattice Boltzmann method on composite grids

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Abstract
A composite block-structured lattice Boltzmann method is proposed for the simulation of two-dimensional incompressible fluid hows. The grid structure is composed of a coarse base grid and one or several fine grid(s). The former covers the entire physical domain; the latter are placed at regions where local grid refinement is desirable. The simulation is first carried out on the base grid level at a smaller relaxation time, allowing a rapid propagation of boundary information throughout the entire domain. Thus large-scale flow features can be resolved efficiently at a relatively low cost. At a later time, fine grid variables are initiated. The dependent variables on both grid levels are, then, advanced in time simultaneously with the fine grid boundary conditions obtained from the base grid solution at the grid interface. As a demonstration, the lid-driven cavity flow is selected for study. The results show good agreement with benchmark numerical data and those calculated from the finite-volume U(2)RANs model. The proposed method is able to produce accurate solutions on fine grids, with a considerable saving in CPU time.