Solutions to acoustic problems are wavelike. The waves are characterized by a wavelength λ in space, whose value depends on the frequency and speed of sound
c in the medium according to
λ = c/f. This wavelength has to be resolved by the mesh.
To represent a wave on a discrete grid (the mesh), it is obvious that the mesh elements must be smaller than the wavelength in order to resolve the wave. That is, there needs to be several degrees of freedom (DOFs) per wavelength in the direction of propagation. In reality, the lower limit for a fully reliable solution lies at about ten to twelve degrees of freedom per wavelength.
When creating an unstructured mesh for use with the default 2nd-order Lagrange elements or 2nd-order serendipity elements (see Lagrange and Serendipity Shape Functions), set the maximum element size
hmax to about
λ/5 or smaller. Because all elements in the constructed mesh are smaller than
hmax, the limit is set larger than the actual required element size. The mesh should also resolve important geometric features and possible gradients in the material parameters and model inputs. After meshing the model, check the total number of DOFs against the model volume and the above guidelines. If the mesh turns out, on average, to be too coarse or too fine, try to change
hmax accordingly.
When using a perfectly matched layer (PML) to truncate the computational domain, it is good practice to use a structured mesh inside the PML region. In 3D models, use a Swept mesh inside the PML and in 2D models use a
Mapped mesh. Use at least 5 elements in the thickness when using rational PML scaling and 8 elements when using the default polynomial scaling in the PML. Again, make sure the check for mesh convergence by adding more layers.
When creating the geometry for your model, use the Layers option to create the geometry of your PML layer or domain. This will ensure that it is suited for proper meshing using a structured mesh.
