Bubble functions for the lattice Boltzmann method and their application to grid refinement

We present a new methodology of velocity field interpolation for the lattice Boltzmann method. The local information on spatial velocity gradients stored in the nodal momentum distribution function is exploited. We achieve quadratic interpolation order between neighboring nodes. Second-order bubble functions are derived from which the off-grid velocity field can be computed. A simple grid-refinement technique based on the bubble functions is introduced.