Collocation-based transfer matrix algorithm for high frequency propagation in a segmented waveguide network

Equations governing the pressure and particle velocity in a sequence of disparate waveguides having arbitrary shapes are derived by a collocation procedure that exactly satisfies junction conditions at a set of points. The ansatz is a modal series whose basis functions describe transverse spatial variation. They are found in an eigenanalysis that satisfies impedance conditions at the walls. The dependent variables are amplitudes of functions that describe modal dependence in the direction of propagation. A solvable set of equations governing these amplitudes in all segments is obtained by combining the junction equations and equations that enforce conditions at the ends of the network. A recursive transfer matrix algorithm that is derived enables sequential solution of the equations for a single junction. An example of two segments, one of whose wall has substantial compliance and resistance, is analyzed by implementing the classical orthogonality method in parallel to the collocation procedure. Results for the modal amplitudes, as well as the pressure and particle velocity distributions along the junction are examined for convergence. Continuity of the particle velocity tangent to a junction, especially in the vicinity of corners, where diffraction is strong, is shown to be an unambiguous indicator of a solution's accuracy.