11.11. Difference-Frequency Generation in Nonlinear Acoustic Waves Governed by the Westervelt Equation

The Westervelt equation, with pressure as a degree of freedom, can be employed to simulate the scattered signal produced by the nonlinear interaction of the primary ultrasound waves at the difference frequency in harmonic analysis.

The harmonic nonlinear acoustics parameters are defined by MP or TB,AFDM,,,,MAT commands. For more information, see Basic Material Parameters of Acoustic Media.

The difference-frequency generation is available for both 2D and 3D acoustic elements FLUID243, FLUID244, FLUID30, FLUID220, and FLUID221 in harmonic analysis. To activate the nonlinear acoustics solver model, one of the following KEYOPT(2) settings:

  • KEYOPT(2) = 8 for the coupled element type

  • KEYOPT(2) = 9 for the uncoupled element type

and the HROPT,HNLA,2 command must be used. For more information, see the HROPT command.

The nonlinear acoustics equations are coupled with the linear structural equation to simulate the fluid-structure interaction (FSI). See Coupling Conditions on the FSI Interface for the FLNS Model in the Theory Reference.

This method can be used with PML, radiation, and impedance boundary conditions to simulate the absorption of outgoing sound waves.

To define the primary frequency waves, the HARFRQ command is used with FREQB and FREQE, where FREQB and FREQE define the two main frequencies. In this analysis model, only three frequencies are considered: the two main frequencies and the difference frequency. Therefore, inputs via the NSUBST command are ignored for this analysis model.

Example 11.14: Nonlinear Acoustics Model Solution for Difference-Frequency Generation

...
! Define viscous-thermal material
MAT_DENS  = 1.204     ! speed of sound
MAT_SONC  = 343.2     ! mass density
MAT_BETA  = 1.2       ! nonlinearity coefficient
MAT_SDIF  = 3.764e-5  ! diffusivity of sound
mp,sonc,1,MAT_SONC
mp,dens,1,MAT_DENS
mp,betw,1,MAT_BETA
mp,sdif,1,MAT_SDIF
...
et,1,244,,8,1	     ! Define nonlinear element type
et,1,244,,8,1,1
...
FREQUENCY2= 40000
FREQUENCY1= 38000
...
!----Velocity BCs
u0=1
lsel,s,line,,1
nsll,s,1
bf,all,velo,,u0
sf,all,port,1
!
...
! Solve the harmonic problem
/solu
...
antype,harmic 
harfrq,FREQUENCY1,FREQUENCY2
hropt,HNLA,2
solve
finish