In this chapter we perform a detailed asymptotic analysis of different numerical
schemes for the interaction between an incompressible fluid and a rigid structure within a
lattice Boltzmann (LB) framework. After introducing the basic ideas and the main tools
for asymptotic analysis of bulk LBM and boundary conditions [19, 21], we concentrate
on moving boundary LB schemes. In particular, we investigate in detail the initialization
of new fluid nodes created by the variations of the computational fluid domain, when
a solid objects moves through a fixed computational grid. We discuss and analyze the
equilibrium-non equilibrium (EnE) refill algorithm [6], reporting comparisons with other
methods, based on numerical and theoretical considerations. Secondly, we focus on force
computation through the Momentum Exchange Algorithm (MEA). Starting from the original
scheme (as proposed in [30]), we introduce a correction which, motivated by the analysis,
improves Galilean invariance properties of the force computation [5, 7, 32]. Moreover,
precise accuracy estimates for the force computation are derived. Our analysis yields first
order accuracy of the global force computation, while it shows that the classical MEA is
not suitable for accurate local forces evaluation. This problem is fixed with the proposed
modification, providing a detailed proof of the accuracy results.
Keywords: Asymptotic analysis, fluid-structure interaction, momentum-exchange algorithm, moving
boundary problems, lattice Boltzmann node re-initialization.
