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Lattice Boltzmann method on quadtree grids.

A lattice Boltzmann method on nonuniform quadtree grids is proposed. Our method employs the interpolation-supplemented lattice Boltzmann model. The advantages of the quadtree grid are preserved by using linear interpolation instead of quadratic interpolation to complete the streaming step in the lattice Boltzmann method. The back-and-forth error compensation and correction (BFECC) method is used to improve the accuracy, so that the second-order accuracy of the conventional lattice Boltzmann method is maintained. Several numerical cases, including a BFECC streaming test, lid-driven cavity flow, and flow over an asymmetrically placed cylinder in a channel, are carried out to demonstrate the accuracy and efficiency of our method.