Cut-cell meshes are an attractive alternative to avoid common mesh generation problems. For hyperbolic problems they pose additional challenges, as elements can become arbitrarily small, leading to prohibitive time step restrictions for explicit time stepping methods. To alleviate this small cell problem we consider a particular stabilization method, the Domain of Dependence (DoD) method. So far, while posessing many favorable theoretical properties, in two dimensions the DoD method was essentially restricted to the transport equation. In this work we extend the DoD method to the acoustic wave equation in two dimensions and provide numerical results for validation.

翻译：切割网格是一种避免常见网格生成问题的颇具吸引力的替代方案。对于双曲问题，此类网格带来了额外挑战，因为网格单元可能变得任意小，从而导致显式时间步进方法的步长限制极为苛刻。为缓解这一"小网格单元"问题，我们考虑了一种特定的稳定化方法——依赖域方法。迄今为止，尽管依赖域方法具有许多良好的理论性质，但在二维空间中，该方法本质上局限于输运方程。在本工作中，我们将依赖域方法扩展至二维声波方程，并提供数值结果以进行验证。