Interpolation – free LBM on non-uniform grids with TRT collision operator

Lattice Boltzmann method (LBM) is a modern numerical scheme for solving fluid dynamics problems. LBM is easy to implement and it has a great potential for modifications. One of the priority LBM development directions is the correct construction of such a scheme on non-uniform spatial grids. However, at the moment, it requires interpolation and often deprives the scheme of the classical LBM advantages. We developed and tested an interpolation-free method for constructing athermal node-based LBM on non-uniform meshes with the TRT collision operator. The method is based on the use of different LBM stencils near the transition boundary of a non-uniform grid, together with a two-step procedure for transformation of populations corresponding to different LBM stencils.