论文标题
一种新的晶格玻尔兹曼计划线性弹性固体：周期性问题
A new lattice Boltzmann scheme for linear elastic solids: periodic problems
论文作者
论文摘要
我们提出了一种新的二阶准确晶格玻尔兹曼方案，该方案在二维中求解线性弹性的准静态方程。与以前的作品相反，我们的公式求解了具有标准速度集的单个分布函数，并避免了对有限差近似值的任何求助。结果，晶格Boltzmann方法的所有计算益处均可用于满负荷。新的方案是使用渐近扩展技术系统地得出的，并提供了对领先误差行为的详细分析。正如线性稳定性分析所证明的那样，该方法对于非常范围的泊松比稳定。我们考虑周期性的问题，专注于管理方程并排除边界条件的影响。通过数值实验和收敛研究来验证分析推导。
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.
