Novel Trends in Lattice-Boltzmann Methods

Book Series: Progress in Computational Physics (PiCP)

Volume 3

by

Matthias Ehrhardt

DOI: 10.2174/97816080571601130301
eISBN: 978-1-60805-716-0, 2013
ISBN: 978-1-60805-717-7
ISSN: 2589-3017 (Print)
ISSN: 1879-4661 (Online)



Indexed in: EBSCO, Ulrich's Periodicals Directory.

Progress in Computational Physics is an e-book series devoted to recent research trends in computational physics. It contains chapters...[view complete introduction]
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Asymptotic Analysis of Lattice Boltzmann Methods for Flow-Rigid Body Interaction

- Pp. 91-126 (36)

Alfonso Caiazzo and Michael Junk

Abstract

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.

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