In this work we review discontinuous Galerkin finite element methods on polytopal grids (PolydG) for the numerical simulation of multiphysics wave propagation phenomena in heterogeneous media. In particular, we address wave phenomena in elastic, poro-elastic, and poro-elasto-acoustic materials. Wave propagation is modeled by using either the elastodynamics equation in the elastic domain, the acoustics equations in the acoustic domain and the low-frequency Biot's equations in the poro-elastic one. The coupling between different models is realized by means of (physically consistent) transmission conditions, weakly imposed at the interface between the subdomains. For all models configuration, we introduce and analyse the PolydG semi-discrete formulation, which is then coupled with suitable time marching schemes. For the semi-discrete problem, we present the stability analysis and derive a-priori error estimates in a suitable energy norm. A wide set of verification tests with manufactured solutions are presented in order to validate the error analysis. Examples of physical interest are also shown to demonstrate the capability of the proposed methods.
翻译:在这项工作中,我们审查了多式网格(PollydG)中多物理波传播现象数字模拟的不连续的Galerkin定数元素方法,以在不同介质中进行多物理波传播现象的数字模拟。特别是,我们处理弹性材料、软弹性材料和软弹性软弹性材料中的波现象。波传播模型使用弹性域的弹性动力学方程式、声学域的声学方程和小弹性方程式中的低频生物方程。不同模型之间的混合是通过(物理上一致的)传输条件实现的。对于所有模型配置而言,我们采用并分析聚变形G半分立配制,然后结合适当的时间演进计划。对于半分辨问题,我们提出稳定性分析,并在适当的能源规范中得出优先误差估计。为了验证错误分析,还提出了一套广泛的核查测试方法,以便验证错误分析。还展示了实际兴趣的例子,以证明拟议方法的能力。