标题： 声波传播/折射通过弥散界面模型 显示英文标题

标题： Acoustic Propagation/Refraction Through Diffuse Interface Models

摘要： 我们提出了一种新颖的方法，通过弱可压缩性公式来模拟穿过由弥散界面分隔的不同介质的声（压力）波传播。 我们的方法基于之前关于不可压缩Navier-Stokes/ Cahn-Hilliard系统的熵稳定间断Galerkin谱元法的工作\cite{manzanero2020entropyNSCH}，并结合了一种修改后的弱可压缩性公式，允许每个相位具有不同的声速。 我们通过数值实验验证了该方法，展示了在一维声传输和反射系数以及二维由斯涅尔定律定义的角度下的谱收敛性。 特别关注于量化弥散界面宽度引入的建模误差。 我们的结果显示，该方法成功捕捉了界面处声波的行为，使透射波呈现指数收敛。 在二维条件下，空气-水条件下的透射角度被准确捕获，直到临界角$13^\circ$。 这项工作代表了在建模不可压缩多相系统中的声传播方面向前迈进了一步，并可能应用于海洋气动声学领域。 显示英文摘要

摘要： We present a novel approach for simulating acoustic (pressure) wave propagation across different media separated by a diffuse interface through the use of a weak compressibility formulation. Our method builds on our previous work on an entropy-stable discontinuous Galerkin spectral element method for the incompressible Navier-Stokes/Cahn-Hilliard system \cite{manzanero2020entropyNSCH}, and incorporates a modified weak compressibility formulation that allows different sound speeds in each phase. We validate our method through numerical experiments, demonstrating spectral convergence for acoustic transmission and reflection coefficients in one dimension and for the angle defined by Snell's law in two dimensions. Special attention is given to quantifying the modeling errors introduced by the width of the diffuse interface. Our results show that the method successfully captures the behavior of acoustic waves across interfaces, allowing exponential convergence in transmitted waves. The transmitted angles in two dimensions are accurately captured for air-water conditions, up to the critical angle of $13^\circ$. This work represents a step forward in modeling acoustic propagation in incompressible multiphase systems, with potential applications to marine aeroacoustics.