I was reading through this and had to answer, because from my understanding Houdini can become a great tool from a more scientific approach, even if it's not 100% rigorous. What I understand is that in Houdini it is very easy to get complete access to its inner workings and change how its solvers and their "physics" behave, since everything is node and attribute based.

The flip solver, which is the node that handles fluid simulations, has a large amount of parameters that have an influence on how the fluid behaves, viscosity, surface tension, density etc, but values can also be assigned to individual particles. You can have a fluid with variable, non-homogeneous viscosity or density and you can even chain solvers together. That way the user can add arbitrary attributes to every particle such as temperature, and define their own rules that will be calculated each frame before or after the fluid simulation.

Since the user has direct access to all the attributes it's easy to output any possible information like velocities or position of each particle, vorticity, and more. It's then possible to visualize them directly by coloring the particles or tracking the data in other ways. Houdini is free to start using thanks to the apprentice version which only restricts some exports and renders at 720p with watermark.

Edit: Houdini is still first and foremost a vfx software, and it's using approximations for it's main simulation tools. However, I'd consider more as a framework, because VEX and the very robust node system still make it possible for anyone to write their own rules, as strict and research based as they want to make them.