Pressure Acoustics, Frequency Domain (acpr)
Time-harmonic acoustic pressure waves (Helmholtz equation). Elmer HelmholtzSolver.
Category |
Acoustics › Pressure Acoustics |
Name (tag) |
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Space dimensions |
3D, 2D, 2D axisymmetric |
Studies |
Frequency Domain |
Dependent variables |
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Default features |
Pressure Acoustics, Initial Values, Sound Hard Boundary (Wall) |
\(\nabla\cdot\left(-\frac{1}{\rho}\nabla p\right) - \frac{k^2}{\rho}p = 0,\quad k=\frac{\omega}{c}\)
Material properties used: Speed of sound (c), Density (ρ).
Interface settings
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Discretization |
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Element order |
Quadratic |
Linear, Quadratic |
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Elmer Solver |
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Additional Elmer solver keywords |
Text (multi-line) |
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Domain features
Pressure Acoustics
Selection: Domains (all by default) · Physics ribbon › Domains, or right-click the interface in the Model Builder
\(\nabla\cdot\left(-\frac{1}{\rho}\nabla p\right) - \frac{\omega^2 p}{\rho c^2} = 0\)
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Pressure Acoustics Model |
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Speed of sound |
c |
From material |
From material, User defined |
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c |
c |
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Expression |
Density |
ρ |
From material |
From material, User defined |
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rho |
ρ |
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Expression |
Boundary features
Sound Hard Boundary (Wall)
Selection: Boundaries (all by default) · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(-\mathbf{n}\cdot\left(-\frac{1}{\rho}\nabla p\right) = 0\)
No settings.
Sound Soft Boundary
Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(p = 0\)
No settings.
Pressure
Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(p = p_0\)
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Pressure |
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Pressure |
p₀ |
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Expression |
Normal Acceleration
Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(-\mathbf{n}\cdot\left(-\frac{1}{\rho}\nabla p\right) = a_n\)
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Normal Acceleration |
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Inward normal acceleration |
aₙ |
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Expression |
Density |
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Density |
ρ |
From material |
From material, User defined |
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rho |
ρ |
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Expression |
Impedance
Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(-\mathbf{n}\cdot\left(-\frac{1}{\rho}\nabla p\right) = -\frac{i\omega p}{Z_i}\)
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Impedance |
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Acoustic impedance |
Zᵢ |
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Expression |
Density |
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Density |
ρ |
From material |
From material, User defined |
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rho |
ρ |
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Expression |
Plane Wave Radiation
Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(-\mathbf{n}\cdot\left(-\frac{1}{\rho}\nabla p\right) + \frac{i k}{\rho}p = 0\)
No settings.
Spherical Wave Radiation
Outgoing spherical (3D, axisymmetric) or cylindrical (2D) waves from the source location; optionally an incident plane wave p_i = p0 exp(-i k d.x) for scattering (total-field formulation).
Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(-\mathbf{n}\cdot\left(-\frac{1}{\rho}\nabla p\right) + \frac{1}{\rho}\left(ik+\frac{1}{r}\right)p = 0\)
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Wave Source |
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Source location, x |
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Expression |
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Source location, y |
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Expression |
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Source location, z |
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Expression |
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Incident Pressure Field |
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Incident pressure field |
None |
None, Plane wave |
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Pressure amplitude |
p₀ |
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Expression |
Wave direction |
+z direction |
+x direction, -x direction, +y direction, -y direction, +z direction, -z direction |
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Exterior Field Calculation
Kirchhoff-Helmholtz integral over the selected closed surface: the pressure anywhere outside it (acpr.efc1.pext, acpr.efc1.Lp_pext) for grids, radiation patterns and directivity plots.
Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(p_{ext}(\mathbf{x}) = \oint_S \left(p\,\frac{\partial G}{\partial n} - G\,\frac{\partial p}{\partial n}\right) dS,\quad G = \frac{e^{-ikR}}{4\pi R}\)
No settings.