Which PDE should I use to simulate different kinds of groundwater flow?

[Atr cheema]

I have learned that diffusion/heat equation can be used to model groundwater flow in confined conditions. Recently I read a paper where they used linear Boussinesq equation (equation 1 in linked paper) to model groundwater flow in unconfined aquifer. Then in another paper, the auther said, he is using non-linear boussinesq equation (equation 1 in 2nd linked paper) to model groundwater flow.
While looking apparently at these equations they look almost same. My question is what is difference between using linear Boussinesq equation and non-linear Boussinesq equation for gw flow modeling as compared to diffusion equation.

 

[Baluncore]

Sorry about the long delay.

The Boussinesq approximations reduce the model by one dimension. That may or may not be an advantage when modelling steady groundwater flow.

Non-linear PDEs model the dispersion of waves at different frequencies. Applicability will depend on if the groundwater flow is steady, or is it seasonally recharged, or cyclically pumped.

Writing PDEs is often easier than identifying the real geometry and the real geological variation you intended to model.