AcousticAbsorbingValue

AcousticAbsorbingValue[pred,vars,pars]

represents a time or frequency domain absorbing boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.

AcousticAbsorbingValue[pred,vars,pars,lkeys]

represents a time or frequency domain boundary condition with local parameters specified in pars[lkey].

Details

  • AcousticAbsorbingValue specifies a boundary condition for AcousticPDEComponent and is used as part of the modeling equation:
  • AcousticAbsorbingValue is typically used to truncate an infinite region to a finite one where the pressure wave is absorbed at the truncation boundary.
  • AcousticAbsorbingValue models a time or frequency domain absorption with dependent variable pressure in , independent variables in and time variable in or frequency variable in .
  • Time-dependent variables vars are vars={p[t,x1,…,xn],t,{x1,…,xn}}.
  • Frequency-dependent variables vars are vars={p[x1,…,xn],ω,{x1,…,xn}}.
  • The time domain acoustics model AcousticPDEComponent is based on a wave equation with time variable , density , sound speed and sound sources and :
  • The frequency domain acoustics model AcousticPDEComponent is based on a Helmholtz equation with angular frequency :
  • The time domain absorbing value AcousticAbsorbingValue with sound source absorbing term in and boundary unit normal models:
  • The frequency domain absorbing value AcousticAbsorbingValue models:
  • Model parameters pars are specified as for AcousticPDEComponent.
  • The dipole source will only be valid within the domain and thus can be excluded from the boundary conditions.
  • The following model parameters pars can be given:
  • parameterdefaultsymbol
    "MassDensity"1, density of media in
    "AcousticSourceDistance"0, inverse source distance in
    "Material"Automatic
    "SoundSpeed"1, speed of sound in
  • With different types of incident waves and a distance in between the wave origin to the boundary , the absorbing boundary condition term in is given by:
  		• plane wave in 1D, 2D, 3D
    		cylindrical wave in 2D, 3D
    		spherical wave in 3D
  • AcousticAbsorbingValue is most efficient when the incident wave is orthogonal to the absorbing boundary.
  • AcousticAbsorbingValue evaluates to a generalized NeumannValue.
  • The boundary predicate pred can be specified as in NeumannValue.
  • An absorbing boundary can be used with:
  • analysis typeapplicable
    Time DomainYes
    Frequency DomainYes
    EigenfrequencyNo
  • If the AcousticAbsorbingValue depends on parameters that are specified in the association pars as …,keypi…,pivi,…], the parameters are replaced with .
  • An alternative to an AcousticAbsorbingValue is a perfectly matched layer (PML) in the time domain or the frequency domain. A perfectly matched layer is preferable when the incident wave is not orthogonal to the absorbing boundary.

Examples

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Basic Examples  (2)

Set up a time domain acoustic absorbing boundary for a plane wave:

Set up a frequency domain acoustic absorbing boundary for a spherical wave:

Scope  (4)

Define model variables vars for a transient acoustic pressure field with model parameters pars and a specific boundary condition parameter:

Define model variables vars for a transient acoustic pressure field with model parameters pars and multiple specific parameters boundary conditions:

Define model variables vars for a transient acoustic pressure field with model parameters pars:

Set up initial conditions ics of a right-going plane wave :

Set up the equation with an acoustic absorbing boundary at the right end for a plane wave:

Solve the PDE:

Visualize the solution:

Define model variables vars for a frequency domain acoustic pressure field with model parameters pars:

Set up the equation with a radiation boundary at the left end and an acoustic absorbing boundary at the right end:

Set up the parametric solver:

Visualize the solution in the frequency domain at various frequencies :

Convert the solution to the time domain:

Wolfram Research (2020), AcousticAbsorbingValue, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticAbsorbingValue.html.

Text

Wolfram Research (2020), AcousticAbsorbingValue, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticAbsorbingValue.html.

CMS

Wolfram Language. 2020. "AcousticAbsorbingValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AcousticAbsorbingValue.html.

APA

Wolfram Language. (2020). AcousticAbsorbingValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AcousticAbsorbingValue.html

BibTeX

@misc{reference.wolfram_2025_acousticabsorbingvalue, author="Wolfram Research", title="{AcousticAbsorbingValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/AcousticAbsorbingValue.html}", note=[Accessed: 22-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_acousticabsorbingvalue, organization={Wolfram Research}, title={AcousticAbsorbingValue}, year={2020}, url={https://reference.wolfram.com/language/ref/AcousticAbsorbingValue.html}, note=[Accessed: 22-February-2025 ]}