In this paper, a highly straightforward approach is presented to simulate acoustic wave propagation in the presence of barriers. This formulation is particularly suited to tackle practical problems requiring the maximisation of noise loss by the optimal location of barriers, since the standard finite element approach has a significant computational burden from remeshing. The discontinuity-enriched elements here proposed are formulated considering very simple manipulations of standard elemental matrices to directly represent the effects of acoustic barriers. The formulation is developed within the context of the partition of unity method but avoids cumbersome enrichment procedures usually required to geometrically describe a strong discontinuity, and enables a very versatile simulation methodology. Embedded discontinuities are modelled independently of the underlying spatial discretisation. Locally-defined degrees of freedom solely related to the elements crossed by the discontinuity are used in the analysis to represent the discontinuous fields. In addition, a locally-defined time-marching formulation is employed to further enhance the solution-finding steps. Numerical applications to sound thin barriers and cracks are presented to assess the performance of the new technique.

在本文中，提出了一种非常简单的方法来模拟在存在障碍的情况下声波的传播。由于标准有限元方法具有重新网格化带来的巨大计算负担，因此该公式特别适用于解决需要通过屏障的最佳位置来最大程度地降低噪声损失的实际问题。考虑到非常简单地处理标准元素矩阵以直接表示声屏障的影响，提出了这里提出的不连续性丰富的元素。该公式是在统一方法的划分范围内开发的，但避免了通常用几何学描述强不连续性所需的繁琐的浓缩程序，并实现了非常通用的仿真方法。嵌入式不连续性的建模与基础空间离散无关。在分析中，仅使用与不连续性所穿过的元素完全相关的局部定义的自由度来表示不连续性场。另外，采用局部定义的时间步调公式来进一步增强求解步骤。提出了声音薄壁障和裂缝的数值应用，以评估新技术的性能。