Does anyone know why they don't use more modern directional representation systems, like curvelets, or shearlets?
My understanding is that they provide optimally sparse representation of this type of data - data that's smooth except on these wavefront sets, and that wavelets perform comparatively poorly.
Maybe a huge amount of legacy code using wavelets that's been debugged and experimentally validated. CFD code checking is laborious and errors often very subtle, and so tends to be pretty conservative.