AcousticPressureCondition
AcousticPressureCondition[pred,vars,pars]
represents a time or frequency domain pressure boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
AcousticPressureCondition[pred,vars,pars,lkey]
represents a time or frequency domain boundary condition with local parameters specified in pars[lkey].
Details
- AcousticPressureCondition specifies a boundary condition for AcousticPDEComponent.
- AcousticPressureCondition is typically used to set a value for the pressure source at the boundary.
- AcousticPressureCondition models a time or frequency domain boundary pressure 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 pressure condition AcousticPressureCondition models
. - The frequency domain pressure condition AcousticPressureCondition models
. - Model parameters pars are specified as for AcousticPDEComponent.
- The following model parameters pars can be given:
-
parameter default symbol "AcousticPressure" 0 
, acoustic pressure in 
- A pressure boundary can be used with:
-
analysis type applicable Time Domain Yes Frequency Domain Yes Eigenfrequency No - AcousticPressureCondition can only be used with an eigenfrequency analysis if it is 0.
- AcousticPressureCondition evaluates to a DirichletCondition.
- The boundary predicate pred can be specified as in DirichletCondition.
- If the AcousticPressureCondition depends on parameters
that are specified in the association pars as …,keypi…,pivi,…, the parameters 
are replaced with 
.
Examples
open all close allBasic Examples (4)
Set up a time domain acoustic pressure boundary:
AcousticPressureCondition[x ≥ 0, {p[t, x, y], t, {x, y}}, <|"AcousticPressure" -> Sin[t]|>]Set up a frequency domain acoustic pressure boundary:
AcousticPressureCondition[x ≥ 0, {p[x, y], ω, {x, y}}, <|"AcousticPressure" -> 1|>]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|>;Define silent initial conditions ics:
ics = {p[0, x] == 0, Derivative[1, 0][p][0, x] == 0};Set up the equation with an acoustic pressure boundary and a pressure source 
of 
at the left end:
eqn = {AcousticPDEComponent[vars, pars] == 0, AcousticPressureCondition[x == 0, vars, pars, <|"AcousticPressure" -> Sin[800π t]|>]};Solve the PDE on a refined mesh:
pfun = NDSolveValue[{eqn, ics}, p, {t, 0, 0.0025}, x∈Line[{{0}, {1}}], Method -> {"PDEDiscretization" -> {"MethodOfLines", "SpatialDiscretization" -> {"FiniteElement", "MeshOptions" -> {"MaxCellMeasure" -> 0.015}}}}];Manipulate[Plot[pfun[t, x], {x, 0, 1}, ...], {{t, 0.001}, 0, 0.0025, 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" -> 1.2|>;Set up the equation with an acoustic pressure boundary at the left, a pressure source 
of 
and an acoustic absorbing boundary at the right:
eqn = AcousticPDEComponent[vars, pars] == AcousticPressureCondition[x == 0, vars, pars, <|"AcousticPressure" -> 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 f:
Manipulate[Plot[Abs[pfun[ω][x]], {x, 0, 1}, ...], {{ω, 1000π, "f"}, {1000π, 1500π, 2000π}}, Rule[...]]Convert the solution to the time domain:
Manipulate[Plot[Re[pfun[ω][x] * Exp[I ω t]], {x, 0, 1}, ...], {{t, 0, "t"}, 0, 0.01}, {{ω, 1000π, "f"}, {1000π, 1500π, 2000π}}, Rule[...]]Scope (2)
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" -> <|"AcousticPressure" -> p1|>|>;
AcousticPressureCondition[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" -> <|"AcousticPressure" -> p1|>, "BoundaryCondition2" -> <|"AcousticPressure" -> p2|>|>;AcousticPressureCondition[x == 0, vars, pars, "BoundaryCondition1"]AcousticPressureCondition[x == 1, vars, pars, "BoundaryCondition2"]Text
Wolfram Research (2020), AcousticPressureCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticPressureCondition.html.
CMS
Wolfram Language. 2020. "AcousticPressureCondition." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AcousticPressureCondition.html.
APA
Wolfram Language. (2020). AcousticPressureCondition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AcousticPressureCondition.html