# Category 17: Acoustic Equations#

These boundary conditions are applied to acoustic equations (Preal, Pimag, Reyn_stress).

## APR#

BC = APR NS <bc_id> <float1> [float2]


### Description / Usage#

(DC/ACOUS_PREAL)

This Dirichlet boundary condition card is used to set constant amplitude of the real part of the acoustic pressure. Definitions of the input parameters are as follows:

APR

Name of the boundary condition (<bc_name>).

NS

Type of boundary condition (<bc_type>), where NS denotes node set in the EXODUS II database.

<bc_id>

The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (node set in EXODUS II) in the problem domain.

<float1>

Value of the real part of the acoustic pressure amplitude.

[float2]

An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not -1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences.

### Examples#

The following is a sample input card:

BC = APR NS 100 1000.0


## APR_PLANE_TRAN#

BC = APR_PLANE_TRAN SS <bc_id> <float1>


### Description / Usage#

(WIC/SCALAR ACOUS_PREAL)

This boundary condition card applies the plane wave transmission conditions to the acoustic wave equations. This card concerns the real part while API_PLANE_TRAN concerns the imaginary component. This condition is used to set reflection/ transmission conditions for a surrounded material that is not being meshed. Definitions of the input parameters are as follows:

APR_PLANE_TRAN

Name of the boundary condition (<bc_name>).

SS

Type of boundary condition (<bc_type>), where SS denotes side set.

<bc_id>

The boundary flag identifier, or a side set number which is an integer that identifies the boundary location (side set in EXODUS II) in the problem domain.

<float1>

$$R_2$$, the acoustic impedance (i.e. product of density and wave speed) in the surrounded material.

### Examples#

The following is a sample input card:

BC = APR_PLANE_TRAN SS 10 0.1


### Technical Discussion#

This condition should be used to account for transmission/reflection conditions for the external boundaries when the acoustic wave equation is used. It reflects characteristics for an acoustic wave encountering a planar interface between two materials;

where k is the acoustic wavenumber and R is the acoustic impedance. The subscript 1 refers to the material inside the external boundary and is the material which is meshed. Subscript 2 refers to the material outside of the external boundary. If $$R_2$$ is set equal to $$R_1$$, then this condition mimics an infinite boundary condition, i.e. no reflection at the external boundary.

## API#

BC = API NS <bc_id> <float1> [float2]


### Description / Usage#

(DC/ACOUS_PIMAG)

This Dirichlet boundary condition card is used to set constant amplitude of the imaginary part of the acoustic pressure. Definitions of the input parameters are as follows:

API

Name of the boundary condition (<bc_name>).

NS

Type of boundary condition (<bc_type>), where NS denotes node set in the EXODUS II database.

<bc_id>

The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (node set in EXODUS II) in the problem domain.

<float1>

Value of the imaginary part of the acoustic pressure amplitude.

[float2]

An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not -1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences.

### Examples#

The following is a sample input card:

BC = API NS 100 1000.0


## API_PLANE_TRAN#

BC = API_PLANE_TRAN SS <bc_id> <float1>


### Description / Usage#

(WIC/SCALAR ACOUS_PIMAG)

This boundary condition card applies the plane wave transmission conditions to the acoustic wave equations. This card concerns the imaginary part while APR_PLANE_TRAN concerns the real component. This condition is used to set reflection/transmission conditions for a surrounded material that is not being meshed. Definitions of the input parameters are as follows:

API_PLANE_TRAN

Name of the boundary condition (<bc_name>).

SS

Type of boundary condition (<bc_type>), where SS denotes side set in the EXODUS II database.

<bc_id>

The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (side set in EXODUS II) in the problem domain.

<float1>

$$R_2$$, the acoustic impedance (i.e. product of density and wave speed) in the surrounded material.

### Examples#

Following is a sample card:

BC = API_PLANE_TRAN SS 10 0.1


### Technical Discussion#

This condition should be used to account for transmission/reflection conditions for the external boundaries when the acoustic wave equation is used. It reflects characteristics for an acoustic wave encountering a planar interface between two materials;

where k is the acoustic wavenumber and R is the acoustic impedance. The subscript 1 refers to the material inside the external boundary and is the material which is meshed. Subscript 2 refers to the material outside of the external boundary. If $$R_2$$ is set equal to $$R_1$$, then this condition mimics an infinite boundary condition, i.e. no reflection at the external boundary.