2026-10-10T06:28:34Z
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2026-09-30T17:40:29Z
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<p>Pointwise validation of the matching conditions.</p>
Muna Elsadig (25145379)
Muhammad Safdar (1474231)
Hala H. Taha (22838328)
Muhammad Afzal (83943)
Biophysics
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whose projection yields
wavepacket &# 8211
wall cosine modes
truncation convergence study
transient treatment follows
precomputed wavenumber grid
form coupling matrix
every matching plane
cavity hybrid resonances
block linear system
power fluxes entering
absorbed power fraction
weighted matrix product
broadband acoustic pulse
membrane &# 8211
dependent acoustic scattering
incident power
vector product
pulse energy
dependent propagation
dependent field
xlink ">
wise reconstruction
velocity continuity
single gaussian
reflection regimes
porous segments
porous model
porous filler
porous core
maximum absorption
lossless limit
fourier approach
field splits
dissipative decay
dissipation audit
computational framework
centre line
<p>Reference frequency Hz with <i>N</i> = 16 acoustic transverse modes and <i>M</i> = 22 Galerkin modes; physical parameters <i>a</i> = 0.05 m, <i>L</i> = 0.10 m, <i>T</i> = 350.0 N/m. Panel (a): real part of the fluid normal velocity in the inlet (dashed) overlaid on the membrane velocity (solid). Panel (b): real part of in the left air cavity (dashed) overlaid on in the porous core (solid). The closed-form elimination of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0358579#pone.0358579.e065" target="_blank">Eq (18)</a> enforces panel (b) to machine precision; panel (a) is convergent in the truncation. Physical interpretation: the membrane velocity matches the inlet fluid normal velocity – confirming the fluid-structure coupling of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0358579#pone.0358579.e044" target="_blank">Eq (9)</a> – and the air-porous pressure jump carries the correct factor from the Delany–Bazley filler.</p>
2026-09-30T17:40:25Z
Image
Figure
10.1371/journal.pone.0358579.g002
https://figshare.com/articles/figure/_p_Pointwise_validation_of_the_matching_conditions_p_/34035780
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