11.10. Nonlinear Acoustics Governed by the Westervelt Equation for Full Harmonic Analysis

The Westervelt equation, with pressure as a degree of freedom, can be used to simulate the nonlinear acoustic wave propagation with high frequency and large amplitude sources 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 harmonic nonlinear acoustics solution 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,1,NH command must be used, where NH represents the number of harmonics, and it must be an integer within the range of 2 and 15. 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.

Unlike transient analysis, in harmonic analysis, the PML can be employed as an absorbing boundary condition.

  • This solution model is only available for a single fundamental frequency input defined by the HARFRQ command. The fundamental frequency, also known as the first harmonic, is assigned by FREQE in the HARFRQ command or FREQB if FREQE is blank.

  • The accuracy of the results can be adjusted by modifying the CNVTOL,PRES command. Reducing this threshold value increases the elapsed time while enhancing accuracy. For more information, see the CNVTOL command.

Example 11.13: Nonlinear Acoustics Model Solution for Full Harmonic Analysis

...
! Define viscous-thermal material for Liver
MAT_DENS  = 1060      ! speed of sound
MAT_SONC  = 1590      ! mass density
MAT_BETA  = 4.4       ! 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	      ! Define nonlinear element type
...
FREQUENCY= 1.0e6
...
!----Pressure BCs
...
d,all,pres,PresBC
...
!Radiation BC
csys,1
nsel,s,loc,x,rx1
nsel,a,loc,z,rz1
sf,all,inf
alls
csys,0
!
...
! Solve the harmonic problem
/solu
...
antype,harmic 
harfrq,FREQUENCY
cnvtol,pres,1.0,1e-5
hropt,HNLA,1,5
solve
finish