  A sparse octree based parallel implementation of the lattice Boltzmann method
for non-uniform meshes is presented in this paper. To couple grids of different
resolutions, a second order accurate compact interpolation is employed and
further extended into three dimensions. This compact interpolation requires
only four source elements from the adjacent level for both two- and three
dimensions. Thus, it reduces the computational and communication overhead in
parallel executions. Moreover, the implementation of a weight based domain
decomposition algorithm and level-wise elements arrangement are explained in
details. The second order convergence of both velocity and strain rate are
validated numerically in the Taylor-Green vortex test case. Additionally, the
laminar flow around a cylinder at Re = 20, 100 and around a sphere at Re = 100
is investigated. Good agreement between simulated results and those from
literature is observed, which provides further evidence for the accuracy of our
method.
