The lattice Boltzmann method (LBM) is a numerical solver for the Navier-Stokes equation, based on an underlying molecular dynamic model. Recently, it has been extended towards the simulation of complex fluids. In this thesis, we use the asymptotic expansion technique to investigate the standard scheme, the initialization problem and possible developments towards moving boundary and fluid-structure interaction problems. At the same time, it will be shown how the mathematical analysis can be used to understand and improve the algorithm. First of all, we elaborate the tool "asymptotic analysis", explaining the methods and the strategy we use for the investigation. A first application to the LBM is described, recovering the approximation of the Navier-Stokes solution starting from the lattice Boltzmann equation. As next, we extend the analysis, to investigate the origin and the dynamic of initial layers. A class of initialization algorithms to generate accurate initial values within the LB framework is described in detail. Then we study the features of a simple moving boundary LBM. In particular, we concentrate on the initialization of new uid nodes created by the variations of the computational fluid domain. Finally, to set up an LBM for uid structure interaction, efficient routines to evaluate forces are required. We describe the Momentum Exchange algorithm (MEA). Precise accuracy estimates are derived, and the analysis leads to the construction of an improved method to evaluate the interface stresses. In conclusion, we test the defined code and validate the results of the analysis on several simple benchmarks.

Asymptotic Analysis of lattice Boltzmann method for Fluid-Structure interaction problems / Caiazzo, Alfonso; relatore: Junk, Michael; relatore esterno: Luo, Li-Shi; Scuola Normale Superiore, 2007.

Asymptotic Analysis of lattice Boltzmann method for Fluid-Structure interaction problems

Caiazzo, Alfonso
2007

Abstract

The lattice Boltzmann method (LBM) is a numerical solver for the Navier-Stokes equation, based on an underlying molecular dynamic model. Recently, it has been extended towards the simulation of complex fluids. In this thesis, we use the asymptotic expansion technique to investigate the standard scheme, the initialization problem and possible developments towards moving boundary and fluid-structure interaction problems. At the same time, it will be shown how the mathematical analysis can be used to understand and improve the algorithm. First of all, we elaborate the tool "asymptotic analysis", explaining the methods and the strategy we use for the investigation. A first application to the LBM is described, recovering the approximation of the Navier-Stokes solution starting from the lattice Boltzmann equation. As next, we extend the analysis, to investigate the origin and the dynamic of initial layers. A class of initialization algorithms to generate accurate initial values within the LB framework is described in detail. Then we study the features of a simple moving boundary LBM. In particular, we concentrate on the initialization of new uid nodes created by the variations of the computational fluid domain. Finally, to set up an LBM for uid structure interaction, efficient routines to evaluate forces are required. We describe the Momentum Exchange algorithm (MEA). Precise accuracy estimates are derived, and the analysis leads to the construction of an improved method to evaluate the interface stresses. In conclusion, we test the defined code and validate the results of the analysis on several simple benchmarks.
2007
MAT/04 MATEMATICHE COMPLEMENTARI
Matematica
fluid-structure interaction
lattice Boltzmann method (LBM)
Mathematics
Navier-Stokes equation
Scuola Normale Superiore
Junk, Michael
Succi, Sauro
Luo, Li-Shi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/85682
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