In general, the maximal mesh size hmax is dictated by the smallest wavelength (the slowest wave) such that
for the default 4th (quartic) order discretization, where fmax is the maximal frequency to resolve in the model, given by the frequency content of the source, and
cmin is the slowest waves speed in the model. This is typically the shear wave speed
cs, but for problems with a free interface or a material discontinuities, interfacial waves also exist. For example, the classical estimate for the Rayleigh wave speed
vR is
where ν is the Poisson’s ratio and
cs is shear wave speed.
The maximal wave speed used to predict the cell wave time scale uses the pressure wave speed cp as default. The value is exact for isotropic materials but is an estimate for materials with anisotropic properties. For anisotropic materials it can be necessary to use a larger value to ensure stability of the numerical method. This can be done in the
Estimate of Maximum Wave Speed section for each material model. To display this section, click the
Show More Options button (
) and select
Advanced Physics Options in the
Show More Options dialog. Select
Automatic (the default) or
User defined. With the
Automatic option the maximum speed is set equal to the pressure wave speed, for
User defined enter another value for
cmax (a larger value may be needed for stability).
When several materials are used in a model, the use of assemblies and pair features is recommended (Continuity and
Pair Acoustic–Structure Boundary, Time Explicit). The advantage of using a pair feature is that the mesh does not need to be conforming on the two sides of the interface (the two parts pf the assembly). This is especially advantageous for the time explicit discontinuous Galerkin method as the time step depends on mesh size and local speed of sound.
If material properties result in large variations of the local cell wave time scale, then it can be advantageous to use the
Adam-Bashforth 3 (local) method instead of the default
Runge-Kutta method.
The Elastic Waves, Time Explicit interface supports physics-controlled mesh. To get an appropriate mesh, remember to set the value of the Maximum frequency to resolve in the
Transient Mesh Settings section. The automatically generated mesh will use this value and an estimate of the slowest wave speed (the default being the shear wave speed), defined in the model, to set up an appropriate mesh that follows the best practices.
On the main Mesh node select the
Sequence Type to be
Physics-controlled mesh and then select the physics interface in the
Contributor list. The
Maximum mesh element size control parameter is either
From physics (it will use the value from the
Transient Mesh Settings section) or
Frequency. For
Frequency enter a value for the
Maximum frequency. Select the
Number of mesh elements per wavelength; for
Automatic this is results 1.5 elements per wavelength, or enter a
User defined value. Finally, select the
Minimum wave speed used to define the shortest wavelength; for
Automatic the shear wave speed is used, for
User defined enter another value, for example, a bending wave speed or a Rayleigh wave speed, if necessary.