Either the Westervelt equation with the pressure degree of freedom or the Kuznetsov equation with the velocity potential degree of freedom can be used to simulate nonlinear acoustic wave propagation from a high frequency and rapidly changing lage amplitude source in a transient analysis. For details and the governing equations, see Nonlinear Acoustics in the Theory Reference.
Nonlinear acoustics parameters are defined by issuing the TB,AFDM,,,,MAT command as detailed in Basic Material Parameters of Acoustic Media.
The nonlinear acoustics solution is available for the 3-dimensional acoustic elements, FLUID30, FLUID220, and FLUID221 in a transient analysis. To activate the nonlinear acoustics solver model, select one of the following KEYOPT(2) settings:
KEYOPT(2) = 8 for the coupled element type
KEYOPT(2) = 9 for the uncoupled element type
Either the pressure-based Westervelt equation (KEYOPT(1) = 0) or the velocity potential-based Kuznetsov equation (KEYOPT(1) = 4) is used to solve the nonlinear acoustics problem in the transient analysis, according to the excitation source in transient applications. Excitation sources for transient analysis are discussed in Applying Excitation Sources and Loads in an Acoustic Analysis.
The nonlinear acoustics equations are coupled with the linear structural equation to simulate the fluid-structure interaction (FSI), see Fluid-Structure Interaction in Nonlinear Acoustics in the Theory Reference.
To capture nonlinear acoustic behavior, it is necessary to mesh the model with 30 DOFs per wavelength rather than 12 DOFs per wavelength in linear acoustics, that is 15 elements per wavelength for higher-order elements and 30 elements per wavelength for lower-order elements.
Nonlinear acoustics modeling does not support perfectly matched layers (PML). Apply either the radiation or impedance boundary condition on the exterior surface of the model to absorb the outgoing sound wave.
The Newmark method is used to solve second-order acoustics nonlinear equations during the nonlinear iteration. Since the damping property of the fluid medium is taken into account in the nonlinear acoustics equations, the nonlinear algorithm presents favorable stability.
In the case of weak damping, stability problems may arise. Numerical instability can
be overcome by introducing artificial numerical damping via the
GAMMA value on the TINTP command.
Example 11.12: Nonlinear Acoustics Model Solution
... ! Define viscous-thermal material c0 = 340.6 ! speed of sound rho = 1.2256 ! mass density delta=2.46r-10*c0**2 ! diffusivity of sound beta=1.2 ! nonlinearity coefficient mp,dens,1,rho mp,sonc,1,c0 tb,afdm,1,,,mat tbfield,time,0 tbdata,1,rho,c0,0,0,0,0 tbdata,7,0,delta,beta ... et,1,220,4,9 ! Define nonlinear element type ... tend=0.4 ! time period dt= 2.5e-4 ! time step ! define velocity excitation Nt=NINT(tend/dt)+1 *dim,_velo,TABLE,Nt,1,1,TIME *do,i,0,Nt _velo(i,0,1)=i*dt _velo(i,1,1)=v0*sin(2*pi*frq*i*dt) *enddo ! apply the normal velocity on inlet nsel,s,loc,z,0 sf,all,shld,%_velo% ! apply the radiation boundary condition on outlet nsel,s,loc,z,L sf,all,inf ... ! Solve the transient problem /solu ... time,tend deltim,dt solve finish