The von Neumann stability analysis along with a Chapman-Enskog analysis is proposed for a single-relaxation-time lattice Boltzmann Method (LBM) for wave propagation in isotropic linear elastic solids, using a regular D2Q9 lattice. Different boundary conditions are considered: periodic, free surface, rigid interface. An original absorbing layer model is proposed to prevent spurious wave reflection at domain boundaries. The present method is assessed considering several test cases. First, a spatial Gaussian force modulated in time by a Ricker wavelet is used as a source. Comparisons are made with results obtained using a classical Fourier spectral method. Both P and S waves are shown to be very accurately predicted. The case of Rayleigh surface waves is then addressed to check the accuracy of the method.

中文翻译：

---

具有规则晶格的弹性固体中波传播的格子 Boltzmann 方法：理论分析和验证

提出了冯诺依曼稳定性分析和 Chapman-Enskog 分析，用于单松弛时间晶格玻尔兹曼方法 (LBM)，用于各向同性线弹性固体中的波传播，使用规则 D2Q9 晶格。考虑了不同的边界条件：周期性、自由表面、刚性界面。提出了一种原始的吸收层模型来防止域边界处的寄生波反射。考虑几个测试案例来评估本方法。首先，使用由 Ricker 小波及时调制的空间高斯力作为源。与使用经典傅立叶光谱方法获得的结果进行比较。P 波和 S 波都显示出非常准确的预测。然后处理瑞利表面波的情况以检查该方法的准确性。