Is it possible, in general, to combine hydrodynamical motion and expansion of material with, say, a finite difference time domain method to simulate light-matter interaction?

If so, how is this done in practice? I guess you would need some kind of operator splitting scheme. If you know more about it, can you suggest me some papers, textbooks, etc.?

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    $\begingroup$ There's a large body of work on this under the name electrohydrodynamics, as well as on the even more popular magnetohydrodynamics (MHD, which describes, e.g., plasma flow). $\endgroup$ – Christian Clason Jan 19 '18 at 14:06
  • $\begingroup$ thanks, that's already helpful. Do you happen to know if there's a library out there which can handle electrokinetics? I was only able to find a bunch of 'static' maxwell-solvers $\endgroup$ – OD IUM Jan 19 '18 at 14:25
  • $\begingroup$ I'm not familiar with any, and I'd be surprised if you found a ready-made, one-size-fits-all solver for such a challenging problem. $\endgroup$ – Christian Clason Jan 19 '18 at 14:44
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    $\begingroup$ On the other hand, it's certainly possible to implement such a solver using libraries such as deal.II or FEniCS, but I'll leave that to the experts to address. $\endgroup$ – Christian Clason Jan 19 '18 at 15:08
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    $\begingroup$ Apologies for another non-answer, but in addition to EHD and MHD, another keyword that may help your search is radiation hydrodynamics or "rad-hydro." $\endgroup$ – Endulum Jan 19 '18 at 16:23

Regarding simulation: There are several commercial solvers that might be helpful.

Regarding numerical techniques themselves:

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