The pressure boundary is a Dirichlet boundary with p = p₀. To apply pressure to the nodes of a finite element model, issue the D,Node,PRES command.

In the poroelastic material model, issue D,Node,PRES to set pressure to zero on free porous surfaces.

nsel,s,loc,z,0.0          ! Select the nodes 
d,all,pres,dispr,dispi    ! Complex pressure 

If using coupled acoustic elements (KEYOPT(2) = 0), avoid zero-pivot warning messages by setting the displacement degrees of freedom (UX, UY, and UZ) at the element nodes not on the interface to zero.

nsel,s,loc,z,0.0       ! Select the nodes 
d,all,ux,0             ! zero ux 
d,all,uy,0             ! zero uy 
d,all,uz,0             ! zero uz 

The rigid wall boundary is a Neumann boundary with applied for the Helmholtz equation solver. It is not necessary to specify a rigid wall boundary condition in an FEM acoustic analysis, as it is a natural boundary condition.

If the pressure spatial distribution can be predicted, the Neumann boundary can be used on the symmetric plane of the model to reduce the model size.

For the viscous-thermal FLNS model, issue the commands D,Node,VX (VY and VZ) and D,Node,TEMP to set the particle velocities and temperature to zero on the rigid wall. For more information, see Boundary Conditions of the FLNS Model in the Theory Reference.

For the poroelastic material model, issue the command D,Node,UX (UY and UZ) to set displacements to zero on the rigid wall. For more information, see Boundary Conditions of Poroelastic Acoustics in the Theory Reference.

Table 7.2: Surface Impedance Boundary Conditions shows surface impedance boundary conditions available for acoustic analysis. The acoustic wave is damped on the impedance boundary, and you can use it to approximate infinity.

Table 7.2: Surface Impedance Boundary Conditions

Boundary Condition	Definition	SF Command Label
Acoustic Infinite Radiation Boundary	Za = ρ0C0	INF
Acoustic Boundary with Absorption Coefficient α		ATTN
Acoustic Impedance Boundary	Za = Za,r + jZa,i	IMPD
Viscous Impedance Boundary in Viscous-Thermal Acoustics	Zv = Zv,r + jZv,i	VIMP
Thermal Impedance Boundary in Viscous-Thermal Acoustics	ZT = ZT,r + jZT,i	TIMP

The acoustic infinite radiation boundary assumes the ratio of the pressure and outward normal velocity is equal to Z₀ = ρ₀C₀. When the radiation boundary is close to the objects or the radiators, the outgoing pressure wave may no longer hold the ratio Z₀ and a numerical error may occur. Using either an absorbing boundary element or artificially matched layers (PML or IPML) is more accurate for modeling the far-field radiation boundary. An infinite radiation boundary can be applied to the nodes of the finite element model via the SF,Nlist,INF command:

nsel,s,ext	! Select exterior node on selected elements
sf,all,inf	! Infinite radiation boundary

The acoustic absorption coefficient is often used to measure the absorption of a surface in acoustic applications. The surface impedance with real value can deviate from the defined absorption coefficient, as shown in Table 7.2: Surface Impedance Boundary Conditions. The absorption coefficient of the surface can be applied to nodes of the finite element model via the SF,Nlist,ATTN,VALUE command:

nsel,s,ext         ! Select exterior node on selected elements
sf,all,attn,0.5    ! Boundary absorption coefficient

A more flexible acoustic complex surface impedance represents the specific ratio between pressure and normal particle velocity on the surface. Surface impedance can be applied to nodes on the finite element model via the SF,Nlist,IMPD,VALUE,VALUE2 command:

nsel,s,loc,z,0         ! Select nodes on inlet
sf,all,impd,z01        ! Impedance on inlet
sf,all,shld,vn         ! Normal velocity on inlet
sf,all,port,10         ! Transparent port
nsel,s,loc,l           ! Select nodes on outlet
sf,all,impd,z02        ! Impedance on outlet

If a complex value is applied to a surface (SF,Nlist,IMPD,VALUE,VALUE2) in an acoustic modal analysis, a negative conductance of admittance is input as VALUE and the product of susceptance and angular frequency is input as VALUE2.

Do not use the SF,Nlist,IMPD command to define the radiation boundary (SF,Nlist,INF) if the pure scattered formulation is selected (ASOL,SC) unless the impedance value is different from the media characteristic impedance Z₀ = ρ₀C₀.

In viscous-thermal acoustics, the viscous impedance (SF,Nlist,VIMP) is defined as the ratio of the shear force and tangential velocity on the surface, and the thermal impedance (SF,Nlist,TIMP) is defined as the ratio of heat flux and temperature on the surface. VIMP and TIMP are in addition to the acoustic impedance (SF,Nlist,IMPD). For more information, see Boundary Conditions of the FLNS Model in the Theory Reference

The free surface (sloshing effect) is taken into account by flagging the plane as a free surface (SF,Nlist,FREE) and defining gravitational acceleration (ACEL).

The free surface must be aligned with the coordinate plane in the global Cartesian coordinate system. The gravitational acceleration input is always positive regardless of how the model is set up.

nsel,s,loc,z,0        ! Select the nodes on the free surface
sf,all,free           ! Flag the nodes on free surface
alls
acel,,,9.85           ! Gravity acceleration in z-direction

In the viscous-thermal FLNS model, issue the command D,Node,VX (VY or VZ) to set the normal velocity to zero on the symmetric plane. Use the NROTAT command prior to the D command if the symmetric planes are not parallel to the coordinate planes of the global Cartesian coordinate system. For more information, see Boundary Conditions of the FLNS Model in the Theory Reference.

csys,11         ! Activate defined local coordinate system
nrotat,all      ! Rotate nodal coord. sys. into active system
nsel,s,loc,y,0  ! Select nodes on the plane
d,all,vy,0      ! Set normal velocity to zero 

For the poroelastic material model, issue the command D,Node,UX (UY or UZ) to set the normal displacement to zero on the sliding surface. Use the NROTAT command prior to the D command if the sliding surfaces are not parallel to the coordinate planes of the global Cartesian coordinate system. For more information, see Boundary Conditions of Poroelastic Acoustics in the Theory Reference.

For the poroelastic material model, issue the command SF,Nlist,PERM to define the permeability on the pervious porous surface. For more information, see Boundary Conditions of Poroelastic Acoustics in the Theory Reference.

nsel,s,ext         ! Select exterior node on selected elements
sf,all,perm,1.e-8  ! Permeability