Asymptotic Analysis of Lattice Boltzmann Methods for Flow-Rigid Body Interaction

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.