LBM on non-uniform grids without interpolation

The lattice Boltzmann method (LBM) is a numerical scheme for solving fluid dynamics problems. One of the important and actively developing areas of LBM is correct construction of the scheme on non-uniform spatial grids. With non-uniform grids the total number of calculations can be significantly reduced. However, at the moment the construction of an LBM scheme near a boundary of grids with different spatial steps inevitably requires data interpolation, which can reduce the LBM approximation order and lead to violation of conservation laws. In this work, for the first time, we have developed and tested a method for constructing an athermal node-based LBM on non-uniform grids without interpolation, with the same time step for grids of different scales. The method is based on a two-stage transformation of populations corresponding to different on-grid stencils.