Theory

The sweep always solves for ALL ports and modes as excitations at once (one factorisation per frequency), so the scattering matrix costs nothing extra; this switch only decides whether it is written out. The solver gives the outgoing modal amplitudes $B$ for unit incident amplitudes. The export scales them with the modal powers so that $\lvert S_{ab}\rvert^2$ is the fraction of the incident power in mode $b$ that leaves as mode $a$ , equation (1). Only propagating modes (positive power) are written. The modal amplitudes of every frequency are also stored in acoustics/results.npz, whether or not the switch is on.

For a model without losses the power-normalised matrix is unitary and, without flow, symmetric (reciprocal).

Equations

S_{ab} = B_{ab}\sqrt{\frac{w_a^{out}}{w_b^{in}}}, \qquad w_m = \frac{S\,\mathrm{Re}(k_{z,m})}{2\rho\omega}

(1)

where	meaning	unit
$S_{ab}$	Power-normalised scattering coefficient from mode $b$ (incident) to mode $a$ (outgoing)	-
$B_{ab}$	Outgoing amplitude of mode $a$ for a unit incident amplitude of mode $b$	-
$w_m$	Power per squared amplitude of mode $m$ at its port (with mean-flow convection: times the convective factor)	W/Pa²
$S$	Port area	m²
$k_{z,m}$	Axial wavenumber	1/m
$\rho$	Density at the port	kg/m³

Default and rule

Default: off
Rule: Off.
Source: The matrix is written from the program's modal solution. Validation: for a straight duct at 5 kHz the six-mode matrix is unitary and reciprocal to $10^{-9}$ .

Valid range on | off

File

Columns f_Hz, row, col, re, im; row and column names are <port>#<mode>. The file grows with the square of the number of modes.

Theory

Equations

Default and rule

Valid range on | off

Related 2