The Pressure Acoustics, Time Explicit Interface
The Pressure Acoustics, Time Explicit (pate) interface (), found under the Acoustics>Pressure Acoustics branch () when adding a physics interface, is used to compute the pressure variation when modeling the propagation of acoustic waves in fluids at quiescent background conditions. The interface is used to solve large transient linear acoustic problems containing many wavelengths. It is suited for time-dependent simulations with arbitrary time-dependent sources and fields. The interface includes a Background Acoustic Field option for modeling of scattering problems. Absorbing layers are used to set up effective nonreflecting-like boundary conditions. The exterior field can be calculated by combining the Exterior Field Calculation feature with a Time to Frequency FFT study step. The interface exists in 2D, 2D axisymmetry, and 3D. Losses at boundaries can be modeled with the Impedance condition. The interface has built-in options that allow setting up frequency dependent impedance conditions in the time domain, by using the very general and flexible General local reacting (rational approximation) impedance option.
The interface is based on the discontinuous Galerkin method (dG-FEM) and uses a time-explicit solver. The method is very memory lean and is well suited for cluster computing. Application areas include the transient propagation of audio pulses in room acoustics or modeling scattering phenomena involving large objects relative to the wavelength.
If the acoustic waves propagate in a background flow, for example, inside a flowmeter, then use The Convected Wave Equation, Time Explicit Interface.
For modeling vibroacoustic problems that involve acoustic structure interaction (ASI) the Pressure Acoustics, Time Explicit interface can be combined with The Elastic Waves, Time Explicit Interface using the Acoustic–Structure Boundary, Time Explicit multiphysics coupling.
The interface solves the linearized Euler equations assuming an adiabatic equation of state. The dependent variables are the acoustic pressure and the acoustic velocity perturbations. Bulk losses (volume attenuation) can be included in the interface using the classical expression for thermal and viscous attenuation or a general dissipation term.
When this physics interface is added, these default nodes are also added to the Model Builder — Pressure Acoustics Time Explicit Model, Sound Hard Boundary (Wall), and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions and source. You can also right-click Pressure Acoustics, Time Explicit to select physics features from the context menu.
For good modeling strategies, meshing, solvers, postprocessing information, acoustics specific plots, as well as tips and tricks, see the Modeling with the Pressure Acoustics Branch (DG-FEM-Based Interface) section.
Domain, Boundary, Edge, and Point Nodes for the Pressure Acoustics, Time Explicit Interface
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Wave-Based Time-Domain Room Acoustics with Frequency-Dependent Impedance. Application Library path Acoustics_Module/Building_and_Room_Acoustics/wave_based_room
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For a tutorial model that uses the interface to model a scattering problem, see the Submarine Scattering: Time-Domain Simulation and FFT tutorial in the COMSOL Application Gallery:
https://www.comsol.com/model/submarine-scattering-time-domain-simulation-and-fft-55921
Settings
The Label is the default physics interface name.
The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is pate.
Filter Parameters for Absorbing Layers
To display this section, click the Show More Options button () and select Advanced Physics Options. In the Filter Parameters for Absorbing Layers section you can change and control the values set for the filter used in the Absorbing Layers. The values of the filter parameters defined here are used in all absorbing layers added to the model and they override the value of filter parameters enabled in the material model (Pressure Acoustics, Time Explicit Model). The default values of the filter parameters α, ηc, and s are set to 0.1, 0.01, and 2, respectively. Inside the absorbing layer it is important to use a filter that is not too aggressive since this will result in spurious reflections.
For general information about the filter see the Filter Parameters section under Wave Form PDE in the COMSOL Multiphysics Reference Manual.
Transient Mesh Settings
Enter a value for the Maximum frequency to resolve fmax (the default is 1000[Hz]). This value is used to set up the physics-controlled mesh for the Pressure Acoustics, Time Explicit interface.
Sound Pressure Level Settings
The settings selected here are only used if the transient solution solved is transformed into the frequency domain using the Time to Frequency FFT study. The zero level on the dB scale varies with the type of fluid. That value is a reference pressure that corresponds to 0 dB. This variable occurs in calculations of the sound pressure level Lp based on the root mean square (rms) pressure prms, such that
where pref is the reference pressure and the star (*) represents the complex conjugate. This is an expression valid for the case of harmonically time-varying acoustic pressure p.
Select a Reference pressure for the sound pressure level based on the fluid type:
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 Use reference pressure for air to use a reference pressure of 20 μPa (20·10−6 Pa).
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 Use reference pressure for water to use a reference pressure of 1 μPa (1·10−6 Pa).
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 User-defined reference pressure to enter a reference pressure pref, SPL (SI unit: Pa). The default value is the same as for air, 20 μPa.
Discretization
In this section you can select the discretization for the Acoustic pressure and Acoustic velocity. Per default both are set to Quartic (4th order). Using quartic elements together with a mesh size equal to approximately half the wavelength to be resolved, leads to the best performance when using the DG method. For further details see the Meshing, Discretization, and Solvers section.
When solving Pressure Acoustics, Time Explicit, it is important to have consistent settings for the Geometry Shape Function and the Discretization of the physics. The Automatic setting for the Geometry shape function (in the Curved Mesh Elements section on the Components node’s settings) may results in a linear geometry representation, if other physics are present in the model. This can lead to numerical errors when solving as the default is to use fourth-order (Quartic) spatial discretization of the dependent variables. To remedy this change the Geometry shape function to Quadratic Lagrange.
If the settings in a model are inconsistent, a warning is given in the solver with the text:
The geometry shape function order is not consistent with the discretization of the dependent variables.
Consider increasing the geometry shape function order to Quadratic Lagrange in the Curved Mesh Element section in the Component node's settings.
Dependent Variables
The dependent variables are the Acoustic pressure, and the Acoustic velocity. The names can be changed, but the names of fields and dependent variables must be unique within a model. The name for the Acoustic velocity, components can also be selected individually.