The Linearized Euler, Frequency Domain (lef) interface (), found under the Acoustics>Aeroacoustics branch () when adding a physics interface, is used to compute the acoustic variations in density, velocity, and pressure in the presence of a stationary background mean-flow that is well approximated by an ideal gas flow. The physics interface is used for aeroacoustic simulations that can be described by the linearized Euler equations.

The equations defined by the Linearized Euler, Frequency Domain interface are the linearized continuity, momentum (Euler), and energy equations. The physics interface solves for the acoustic variations in the density ρ, velocity field u, and pressure p. The equations are formulated in the frequency domain and assume harmonic variation of all sources and fields. The harmonic variation of all fields and sources is given by eiωt using the +iω convention. The background mean flow can be any stationary gas flow that is well approximated by an ideal gas. The coupling between the acoustic field and the background flow does not include any predefined flow-induced noise. Even though the equations do not include any loss mechanisms, only acoustic modes exist in the frequency domain as the driving frequency is predefined and real valued.

Coupling between a background mean flow, computed from a Fluid Flow model, and the Linearized Euler model is handled by the Background Fluid Flow Coupling multiphysics coupling and the dedicated Mapping study. Details are also found in the Mapping Between Fluid Flow and Acoustics Mesh section.

The equations are implemented in the so-called scattered field formulation. All equations and boundary conditions are formulated in the total acoustic fields (ρt, ut, pt). The total fields are in the presence of the Background Acoustic Fields feature the sum of the background (ρb, ub, pb) and the scattered field (ρ, u, p):

When this physics interface is added, these default nodes are also added to the Model Builder — Linearized Euler Model, Rigid Wall, and Initial Values. For axisymmetric components an Axial Symmetry node is also added.

Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions and sources. You can also right-click Linearized Euler, Frequency Domain to select physics features from the context menu.

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 lef.

See Sound Pressure Level Settings for the Pressure Acoustics, Frequency Domain interface. Only Use reference pressure for air or User-defined reference pressure are available selections.

Enter a value or expression for the Typical wave speed for perfectly matched layers cref (SI unit m/s). The default is lef.c0 and the value is automatically taken from the material model. If several materials or material models are used it is best practice to add one PML for each. This will ensure that the typical wavelength is continuous within each PML feature.

For convected acoustic problems, it can be necessary to set the value of the Typical wavelength from option in the PML feature manually, to correct for the convected background velocity.

This physics interface defines these dependent variables (fields), the Density rho, Velocity field u and its components, and Pressure p. The name can be changed but the names of fields and dependent variables must be unique within a model.

To display this section, click the Show More Options button () and select Stabilization in the Show More Options dialog box.

Select the Stabilization Method — No stabilization applied, Galerkin least squares (GLS) stabilization (the default), Streamline upwind Petrov-Galerkin (SUPG) stabilization, or Streamline diffusion (legacy method). When stabilization is selected enter a value for the Stabilization constant αstab (dimensionless). The default value is 1e-5 and should typically have a numerical value between 1e-3 and 1e-7. In cases where there is no background flow, set the value to the lower limit 1e-7.

The default GLS stabilization is the most efficient stabilization method as it operates on the convective and reactive parts of the governing equations. This is also the default method and the method suggested for most applications. The stabilization constant αstab can be tuned depending on the problem solved, the nature of the background mean flow, and on the computational mesh.

If the stabilization is turned off (when No stabilization applied is selected), it is recommended to change the discretization (see section below) to ensure a stable numerical scheme; set the order of the pressure one order lower than the velocity and density dependent variables, for example, using a P2-P2-P1 discretization.

From the list select the element order and type (Lagrange or serendipity) for the density, velocity, and pressure degrees of freedom. The default is Linear for all the dependent variables.