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30 Axial coordinate 50 Exact solution acoustic disturbances acoustic impedance acoustic velocity additional condition attenuation axial propagation axial propagation constant boundary condition boundary nodes broadband jet noise broadband suppression Comparison of planar component of acoustic computational domain decibels eigenfunctions element solution 20 error vector Exact solution Finite excellent correlation exhaust jet finite element method Finite element solution fluid global matrix HSCT Hz and Mq identity matrix Imaginary solution inflow boundary irrotational Langley Research Center linear relationship lined ejector mathematical model modal solution normal component numerical method obtained optimization studies Optimized uniform liner outflow boundary planar acoustic pressure predicting pressure at 5000 Real solution rigid wall duct segmented liner solution 20 30 solution Finite element sound field steady flow field subsonic and supersonic subsonic flow supercomputer supersonic Mach number tangential component transient wave transverse component uniform flow uniform liner tuned variable impedance liners vortical flow wall lining