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

被引：8

作者：

Boolakee, Oliver ^{[1
]}

Geier, Martin ^{[2
]}

De Lorenzis, Laura ^{[1
]}

机构：

[1] Swiss Fed Inst Technol, Dept Mech & Proc Engn, CH-8092 Zurich, Switzerland

[2] TU Braunschweig, Inst Computat Modeling Civil Engn, D-38106 Braunschweig, Germany

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2023年 / 404卷

关键词：

Lattice Boltzmann method; Asymptotic expansion; Linear elasticity; Stability analysis; WAVE-PROPAGATION; EQUATION; STABILITY; MODELS;

D O I：

10.1016/j.cma.2022.115756

中图分类号：

T [工业技术];

学科分类号：

08 ;

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.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页数：32

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