Bilbao Stefan
Acoustics and Audio Group, University of Edinburgh, Room 2.10 Alison House, 12 Nicolson Square, Edinburgh EH8 9DF, United Kingdom.
J Acoust Soc Am. 2023 Aug 1;154(2):874-885. doi: 10.1121/10.0020635.
One of the main challenges in time domain wave-based acoustics is the accurate simulation of both boundary conditions and barriers capable of reflecting and transmitting energy. Such scattering structures are generally of irregular geometry and characterised in terms of frequency-dependent reflectances and transittances. Conditions for numerical stability can be difficult to obtain in either case. Immersed boundary methods, which are heavily used in computational fluid dynamics applications, replace boundaries by discrete driving terms, avoiding volumetric meshing and staircasing approaches altogether. The main contribution of this article is a unified numerical treatment of both impedance boundary conditions and barriers capable of transmitting energy and suitable for use in the setting of wave-based acoustics. It is framed in terms of the immersed boundary method within a finite difference time domain scheme, using a dual set of matched discrete driving terms in both the conservation of mass and momentum equations that can be tuned against a desired reflectance or transmittance. Numerical results in three dimensions are presented, illustrating non-porous barriers and impedance boundary conditions, and highlight important features such as spurious leakage through an immersed boundary. A brief demonstration of conditions for numerical stability of the immersed boundary method in this context is provided in an appendix.
基于时域波动的声学中的主要挑战之一是准确模拟能够反射和传输能量的边界条件和障碍物。此类散射结构通常具有不规则的几何形状，并根据频率相关的反射率和透射率来表征。在这两种情况下，都可能难以获得数值稳定性条件。在计算流体动力学应用中大量使用的浸入边界方法，通过离散驱动项来代替边界，完全避免了体网格划分和阶梯式方法。本文的主要贡献是对阻抗边界条件和能够传输能量且适用于基于波动声学设置的障碍物进行统一的数值处理。它是在有限差分时域方案内根据浸入边界方法构建的，在质量守恒和动量方程中使用一组双重匹配的离散驱动项，这些驱动项可以根据所需的反射率或透射率进行调整。给出了三维数值结果，展示了无孔障碍物和阻抗边界条件，并突出了诸如通过浸入边界的虚假泄漏等重要特征。附录中提供了在此背景下浸入边界方法数值稳定性条件的简要说明。
