Having used Fluent and COMSOL in the past, I recently switched to an open-source CFD package called OpenFOAM. Although I use the label "CFD" software, it really allows you to solve PDEs.
It has basic meshing functionality (blockMesh), and integrates well into a reasonably well-developed visualization tool called ParaView. However, the pre- and post-processing steps can be carried out using any of your favorite programs - free or commercial. There are all sorts of converters available to translate data to and from these applications to something that OpenFOAM understands.
What is great about the program, and the primary reason I am attracted to it, is the flexibility of the solver. It allows one to extend standard solvers to consider a new constitutive relation, or a new multi-physics problem, relatively easily.
As bonus, it has great parallel efficiency, and is of course free!
Unlike most of the other FOSS software that I use, I like OpenFOAM more for the "open-source" part, than the "free" part, since writing/changing source code is critical to solve my problem.
I've started working on an interesting problem of the flow of a nanotube filled polymer resin in a relatively simple geometry, where the constitutive relation depends on the density and orientation of the nanotubes, which is in turn governed by the flow field, and hence, the constitutive relation.
Here are a few links that I found useful, while trying to ascend the relatively gradual learning curve (I am still climbing!)
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