1. Reference problem#

1.1. Geometry#

x

y

z

_images/100009C400001E2E00001727C67CC693769D0E35.svg

Dimensions of the waterproof and rigid tank:

g height: \(H=0.3m\); length: \(L=0.8m\); width: \(l=0.1m\).

1.2. Material properties#

The material modelled is the homogeneous fluid contained in the tank:

  • density: \({\rho }_{c}=1000\mathrm{kg}/{m}^{3}\);

  • speed of sound: \(c=1400m/s\).

Gravity is: \(g=\mathrm{9,81}m/{s}^{2}\).

1.3. Boundary conditions and loading#

The bottom and the side faces are waterproof and fixed. In the formulation fluctuating pressure + fluctuating displacement potential \((P,\mathrm{\Phi })\) in linear acoustics of a barotropic medium, it is therefore useless to impose any condition on these walls. The same applies to the fluctuating pressure formulation alone. The free surface subjected to the action of gravity is affected by a linear modeling of sloshing waves (gravity) in the 1st order of AIRY (or STOKES) via finite elements \((P,\mathrm{\Phi },z)\). On the other hand, if we neglect this phenomenon, in the formulation fluctuating pressure + potential, we will have to assign the boundary condition over the entire free surface: \((P,\mathrm{\Phi })=(\mathrm{0,0})\), cf. < https://code-aster.org/V2/doc/default/fr/man_r/r4/r4.02.02.pdf>` [R4.02.02]] `_.