A new lattice Boltzmann scheme for linear elastic solids: periodic problems

作     者：Boolakee, Oliver Geier, Martin De Lorenzis, Laura 

作者机构：Department of Mechanical and Process Engineering ETH Zürich Zürich8092 Switzerland Institute for Computational Modeling in Civil Engineering TU Braunschweig Braunschweig38106 Germany 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Distribution functions 

摘      要：We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a standard velocity set and avoids any recourse to finite difference approximations. As a result, all computational benefits of the lattice Boltzmann method can be used to full capacity. The novel scheme is systematically derived using the asymptotic expansion technique and a detailed analysis of the leading-order error behavior is provided. As demonstrated by a linear stability analysis, the method is stable for a very large range of Poisson s ratios. We consider periodic problems to focus on the governing equations and rule out the influence of boundary conditions. The analytical derivations are verified by numerical experiments and convergence studies. © 2022, CC BY.