Geometry and domain decomposition for the ChC method. The duct height is and only the lower symmetrical half is solved. The cavity is covered by a membrane and is filled with a sound absorption material of dimensional flow resistivity .
Comparison of the error for the transmitted wave between the spectral method of ChC and the FD4. The sandwiched segment has , , and . is the number of grids per wavelength.
Comparison of convergence for three methods for a drumlike silencer with the parameter setting of Eq. (23) and . (a) Energy conservation error for FEM and ChC. (b) Contour of the truncation error of FGa measured in TL relative to the most accurate result calculated by ChC with . (c) The slow FGa convergence with respect to for .
Comparison of FGa (solid line, ) and ChC solutions (-○-, ) for (a) vertical particle velocity across the duct and for (b) fluid loading along the membrane.
(a) The capturing of a spectral peak using FGa (dashed lines) of various numbers of modes and ChC with various ranging from 4 (solid line) and 6 (open circles) to 16 (solid line). (b) Vertical acoustic particle velocity distribution in the duct for the peak frequency of 0.126 804 991 with .
Comparison of (a) accuracy and (b) CPU time performance between ChC and FEM for a dissipative system at high frequency. The parameters are set in Eq. (24).
Calibration of the DtN boundary condition by comparison with the known solution, Eq. (30), for the higher-order duct acoustics modes. The square domain of size is discretized by Gauss–Lobatto grids.
Spectral comparison between the optimal membrane covered duct lining with , , and the optimal pure duct lining with .
Acoustic field for a membrane covered duct lining for the best setting for , , and . (a) SPL distribution in the duct passage. (b) Vertical velocity distribution in the duct (upper) and cavity (lower) regions, joined together by the membrane interface.
Analysis of the effect of membrane on the lining. (a) Sound intensity across the membrane interface. (b) Plane-wave mode variation with distance. (c) First mode for the half-passage as defined by Eq. (33).
List of solutions required in the domain decomposition method.
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