Analysis of lattice Boltzmann nodes initialisation in moving boundary problems

The lattice Boltzmann method (LBM) is a numerical scheme based on a fixed grid. Dealing with moving boundary problems, proper routines are needed to initialise the variables at the new nodes, created by the variations of the computational fluid domain. We use asymptotic analysis to investigate the problem and possible solutions. A simple algorithm is proposed, able to achieve the same accuracy as the standard LBM. The theoretical predictions are tested on simple benchmarks