The movement of water waves is a topic of interest to researchers from different areas. While their propagation is described by Euler equations, there are instances where simplified models can also provide accurate approximations. A well-known reduced model employed to study the wave dynamics is the Boussinesq model. Despite being extensively studied, to our knowledge, there is no research available on a Boussinesq model featuring a sponge layer. Therefore, in this work, we present a Boussinesq model with a sponge layer. Furthermore, we carry out a numerical investigation to explore the advantages and limitations of the proposed model. For this purpose, we compare the numerical solutions of the model with and without the sponge in three different scenarios. The numerical solutions are computed by a pseudospectral method. Our results show that the Boussinesq model with a sponge layer is numerically stable and advantageous because it is able to absorb low-amplitude waves, allowing it to run the numerical simulations for long periods of time without requiring a large spatial domain, but it is not able to absorb high-amplitude waves.

翻译：水波运动是不同领域研究者关注的课题。尽管其传播过程由欧拉方程描述，但在某些情况下，简化模型也能提供精确近似。用于研究波浪动力学的著名简化模型之一是Boussinesq模型。尽管该模型已被广泛研究，但据我们所知，目前尚无关于含海绵层Boussinesq模型的研究。因此，本文提出一种含海绵层的Boussinesq模型，并通过数值研究探讨该模型的优势与局限性。为此，我们在三种不同场景下对比了有、无海绵层模型的数值解。数值解通过伪谱方法计算。结果表明，含海绵层的Boussinesq模型具有数值稳定性及优势：它能吸收低振幅波，从而在无需大空间域的条件下长时间进行数值模拟，但无法吸收高振幅波。