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108 I. Sazonov et al.
6.4 Scattering by a PEC NACA0012 Aerofoil
The next example involves the simulation of scattering of a plane single frequency
wave, directed along the x-axis, by a perfectly conducting NACA0012
aerofoil of length λ. The aim of this example is to analyse the performance
of the numerical schemes when the geometry exhibits high curvature. A
benchmark solution is computed using an unstructured mesh with spacing
λ/120. The unstructured mesh is generated, outside the aerofoil, in the region
−λ ≤ x, y ≤ λ. The scattering width distributions computed on this
mesh with the co-volume scheme and the FETD scheme proved to be identical.
An unstructured mesh was generated to meet the spacing requirement
of λ/15. Another unstructured mesh, providing better representation of the
leading edge curvature, is generated by locally reducing the mesh spacing in
the vicinity of the leading edge of the airfoil by a factor of 2. A view of both
these meshes is shown in Figure 11.
The computed scattering width distributions are compared with the benchmark
distribution in Figure 12. It can be observed that the co-volume results
are better on the uniform mesh and that the accuracy of the FETD results improve
with the local refinement in the leading edge region. For this example,
Table 4 shows the values of spc, time and E SW . The co-volume method is
approximately 30 times faster than FETD for this example.
6.5 Scattering by a PEC Cavity
The final example considers the simulation of scattering of a plane single
frequency wave by a U-shaped PEC cavity. The thickness of the cavity walls
is equal to 0.4λ, the internal cavity width is 2λ and the internal cavity length
is 8λ. In the simulation, the wave is incident upon the open end of the cavity
and propagates in a direction which lies at an angle θ =30 ◦ to the main
axis of the cavity. An unstructured mesh is employed, with typical spacing
λ/15, in the region that lies within a distance of λ from the scatterer, as
(a)
(b)
Fig. 11. Details of the unstructured meshes employed for the simulation of scattering
of a plane TE wave by a PEC NACA0012 aerofoil of length λ showing (a) the
uniform mesh, (b) the locally refined mesh.