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Autori principali: Boolakee, Oliver, Geier, Martin, De Lorenzis, Laura
Natura: Preprint
Pubblicazione: 2024
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Accesso online:https://arxiv.org/abs/2408.01081
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author Boolakee, Oliver
Geier, Martin
De Lorenzis, Laura
author_facet Boolakee, Oliver
Geier, Martin
De Lorenzis, Laura
contents We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Boltzmann formulation is introduced. The only difference to conventional lattice Boltzmann formulations is the usage of vector-valued populations, so that all computational benefits of the algorithm are preserved. Using the asymptotic expansion technique and the notion of pre-stability structures we further establish second-order consistency as well as analytical stability estimates. Lastly, we introduce a second-order consistent initialization of the populations as well as a boundary formulation for Dirichlet boundary conditions on 2D rectangular domains. All theoretical derivations are numerically verified by convergence studies using manufactured solutions and long-term stability tests.
format Preprint
id arxiv_https___arxiv_org_abs_2408_01081
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Lattice Boltzmann for linear elastodynamics: periodic problems and Dirichlet boundary conditions
Boolakee, Oliver
Geier, Martin
De Lorenzis, Laura
Numerical Analysis
We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Boltzmann formulation is introduced. The only difference to conventional lattice Boltzmann formulations is the usage of vector-valued populations, so that all computational benefits of the algorithm are preserved. Using the asymptotic expansion technique and the notion of pre-stability structures we further establish second-order consistency as well as analytical stability estimates. Lastly, we introduce a second-order consistent initialization of the populations as well as a boundary formulation for Dirichlet boundary conditions on 2D rectangular domains. All theoretical derivations are numerically verified by convergence studies using manufactured solutions and long-term stability tests.
title Lattice Boltzmann for linear elastodynamics: periodic problems and Dirichlet boundary conditions
topic Numerical Analysis
url https://arxiv.org/abs/2408.01081