TY - JOUR
T1 - Modeling impedance boundary conditions and acoustic barriers using the Immersed Boundary Method
T2 - The three-dimensional case
AU - Bilbao, Stefan
N1 - Publisher Copyright:
© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
PY - 2023/8/11
Y1 - 2023/8/11
N2 - 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 3D 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.
AB - 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 3D 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.
UR - https://pubs.aip.org/asa/jasa
U2 - 10.1121/10.0020635
DO - 10.1121/10.0020635
M3 - Article
SN - 0001-4966
VL - 154
SP - 874
EP - 885
JO - The Journal of the Acoustical Society of America
JF - The Journal of the Acoustical Society of America
IS - 2
ER -