Axisymmetric Horn¶

Problem description¶

This example solves adaptively the pressure field in a 3D axisymmetric model of a harmonic acoustic horn. The geometry and initial mesh are shown below.

Equation solved:

$-\nabla \left(\frac{1}{\rho} \nabla p\right) - \frac{1}{\rho}\left(\frac{\omega}{c}\right)^2 p = 0.$

Boundary conditions are Dirichlet (prescribed pressure) on the bottom edge, zero Neumann (symmetry) on the left edge, Newton (matched boundary)

$\frac{1}{\rho} \frac{\partial p}{\partial n} = \frac{j \omega p}{\rho c}$

on the outlet arc and zero Neumann (wall) on the rest of the boundary. Here $p$ is pressure, $\rho$ density of air, $\omega = 2 \pi f$ angular frequency, and $c$ speed of sound. See the main.cpp file for concrete values.