Apartment¶
Git reference: Example apartment.
Model problem¶
This example solves adaptively the pressure field in an apartment, that is caused by a harmonic local acoustics source. 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 one edge. The rest of the boundary are wall with a Newton condition (matched boundary).
\frac{1}{\rho} \frac{\partial p}{\partial n} = \frac{j \omega p}{\rho c}
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.
Weak forms¶
class CustomWeakFormAcoustics : public WeakForm
{
public:
CustomWeakFormAcoustics(std::string bdy_newton, double rho,
double sound_speed, double omega)
: WeakForm(1) {
scalar ii = cplx(0.0, 1.0);
// Volumetric terms.
add_matrix_form(new DefaultLinearDiffusion(0, 0, 1.0/rho,
HERMES_SYM));
add_matrix_form(new DefaultLinearMass(0, 0, - sqr(omega) / rho / sqr(sound_speed),
HERMES_SYM));
// Term generated by the Newton condition at outlet.
add_matrix_form_surf(new DefaultMatrixFormSurf(0, 0, bdy_newton,
-ii * omega / rho / sound_speed));
};
};
