Dear Yu Ma,
You are correct that the current version of HydroDyn is based on linear (first-order) wave-body hydrodynamics. You are also right that second-order hydrodynamics could be important for semi-submersibles and barges; it could also be important for spar buoys and tension-leg platforms (TLPs).
We have recently started a project to upgrade HydroDyn to include second-order hydrodynamics for floating platforms. Second-order wave-excitation loads will be implemented by reworking the HydroDyn module to (1) input second-order frequency-domain quadratic-transfer functions (QTF) preprocessed through WAMIT and (2) transform the loads to the time domain based on the specified irregular wave spectrum and directional spreading. The implementation will include bichromatic and bidirectional (short-crested) wave components in finite depth water. The complete second-order solution will be superimposed on the first-order and viscous drag terms currently computed in HydroDyn. But because this project is just getting started, it will be a while before this version is completed and released.
Best regards,