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:
-
parameter default symbol "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: -
Wolfram Language code: [image]plane wave in 1D, 2D, 3D 
Wolfram Language code: [image]cylindrical wave in 2D, 3D 
Wolfram Language code: [image]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 type applicable Time Domain Yes Frequency Domain Yes Eigenfrequency No - 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
open all close allBasic Examples (2)
Set up a time domain acoustic absorbing boundary for a plane wave:
AcousticAbsorbingValue[x ≥ 0, {p[t, x, y], t, {x, y}}, <||>]Set up a frequency domain acoustic absorbing boundary for a spherical wave:
AcousticAbsorbingValue[x ≥ 0, {p[x, y, z], ω, {x, y, z}}, <|"MassDensity" -> ρ, "SoundSpeed" -> c, "AcousticSourceDistance" -> 1 / r|>]Scope (4)
Define model variables vars for a transient acoustic pressure field with model parameters pars and a specific boundary condition parameter:
vars = {p[t, x, y], t, {x, y}};
pars = <|"SoundSpeed" -> 343, "MassDensity" -> 12 / 10, "BoundaryCondition1" -> <|"AcousticSourceDistance" -> 1 / r|>|>;
AcousticAbsorbingValue[x == 1, vars, pars, "BoundaryCondition1"]Define model variables vars for a transient acoustic pressure field with model parameters pars and multiple specific parameters boundary conditions:
vars = {p[t, x, y], t, {x, y}};
pars = <|"SoundSpeed" -> 343, "MassDensity" -> 12 / 10, "BoundaryCondition1" -> <|"AcousticSourceDistance" -> 1 / r|>, "BoundaryCondition2" -> <|"AcousticSourceDistance" -> 0|>|>;AcousticAbsorbingValue[x == 0, vars, pars, "BoundaryCondition1"]AcousticAbsorbingValue[x == 1, vars, pars, "BoundaryCondition2"]Define model variables vars for a transient acoustic pressure field with model parameters pars:
vars = {p[t, x], t, {x}};
pars = <|"SoundSpeed" -> 343, "MassDensity" -> 1.2|>;Set up initial conditions ics of a right-going plane wave 
:
p0 = D[0.125 Erf[(x - 0.5) / 0.15], x];
ics = {p[0, x] == p0, Derivative[1, 0][p][0, x] == -343 * D[p0, x]};Set up the equation with an acoustic absorbing boundary at the right end for a plane wave:
eqn = AcousticPDEComponent[vars, pars] == AcousticAbsorbingValue[x == 1, vars, pars];pfun = NDSolveValue[{eqn, ics}, p, {t, 0, 0.003}, x∈Line[{{0}, {1}}]];Manipulate[Plot[pfun[t, x], {x, 0, 1}, ...], {{t, 0.0013}, 0, 0.003, 10 ^ -4}, Rule[...]]Define model variables vars for a frequency domain acoustic pressure field with model parameters pars:
vars = {p[x], ω, {x}};
pars = <|"SoundSpeed" -> 343, "MassDensity" -> 12 / 10|>;Set up the equation with a radiation boundary at the left end and an acoustic absorbing boundary at the right end:
eqn = AcousticPDEComponent[vars, pars] == AcousticRadiationValue[x == 0, vars, pars, <|"SoundIncidentPressure" -> 1|>] + AcousticAbsorbingValue[x == 1, vars, pars]pfun = ParametricNDSolveValue[eqn, p, x∈Line[{{0}, {1}}], {ω}];Visualize the solution in the frequency domain at various frequencies 
:
Plot[Table[Legended[Abs[pfun[ω][x]], ω], {ω, {1000π, 1500π, 2000π}}]//Evaluate, {x, 0, 1}, ...]Convert the solution to the time domain:
Plot[Table[Legended[Re[pfun[ω][x] * Exp[I ω t]], ω], {t, {0.01}}, {ω, {1000π, 1500π, 2000π}}]//Evaluate, {x, 0, 1}, ...]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