It just happens to be very complicated. You're right in that it's a mixture of E&M, thermodynamics, and fluid mechanics. Whether it becomes computationally prohibitive to model is something I am unsure of, but may be possible with some simplifying assumptions.
Edit: after a bit more research, I found a paper where, if I follow correctly, they are laying out a framework for creating such a model: http://arxiv.org/abs/1004.1611
Seriously? Except its not a plasma, its a fluid, and computational fluid dynamics (CFD) simulations don't include (at this stage) electromagnetic forces. Show me a paper that can describe a fluid in motion where the force on each element is computed as a function of the electromagnetic state, the thermal state, and the viscosity state of each other element and I'll show you a candidate for a Nobel prize.
At least in the open literature I haven't seen CFD models that consider the influence of elements beyond a few centimeters, the magnetic forces in the Earth's core move elements meters, if not kilometers, away so the date sets do get very strange, and you have to mix in that if they cool to much or you hit an eddy current and the pressure drops the current gets cut off and the electrodynamic forces stop.
If you can blend that with a CFD simulation and then add in the changes in conductivity as the material goes in an out of its conductive and non-conductive modes sure.
Its the latter bit that seems so mind bending to me. MHD simulations start with a plasma and it can be conducting throughout the simulation in all places.
CFD simulations deal with the forces between elements that express as viscosity, turbulent, and laminar flows.
MHD assumes that elements in the flow are always affected by the electro-magnetic forces in play, CFD doesn't account for electro-magnetic forces.
CFD assumes that the elements in the flow are only affected by the forces of nearby elements and not the actions or state of elements that are further away.
An FeO simulation has to combine them somehow, and account for whorls and eddies converting elements from the MHD domain into the CFD domain and then back again.
Anyway, I am looking forward to the papers on this stuff. It combines two areas I enjoy, complex systems and physics!
Magnetohydrodynamics (MHD) is the combination of Maxwell's Equations in a moving frame of reference and The Navier Stokes Equation. So it includes both the impact of inertial and electromagnetic forces of the flow. MHD is the long wavelength limit of kinetic (particle) plasma theory. The Earths core has in the past been modeled as an MHD fluid but it is usually assumed to be incompressible. I am not aware of compressible models but I have not worked in this field in a decade.
It just happens to be very complicated. You're right in that it's a mixture of E&M, thermodynamics, and fluid mechanics. Whether it becomes computationally prohibitive to model is something I am unsure of, but may be possible with some simplifying assumptions.
Edit: after a bit more research, I found a paper where, if I follow correctly, they are laying out a framework for creating such a model: http://arxiv.org/abs/1004.1611