Depends.
Normally, the movement in the core is slow enough so that the neutronics and the movement are timely decoupled. Then you can treat the neutronics as steady state. In the next step, use an appropriate code (CFD or whatever) to calculate where a fluid element is moving after a certain time (the distance you can allow it to travel depends on the flux / power density gradients in your core). Then, do another steady state neutronic calculation. Probably you want to use an algorithm which is stable in time in a higher order.
If it is not possible to decouple neutronics and core movement, then probably a new code has to be developed (or an existing one adjusted).
Normally, the core movement is highly considered for thermal hydraulic calculations.
The analysis tools already exist for the Pebble Bed Reactor, where the TRISO fuel travels down through the core like a gumball machine (LOL). The Germans developed tools based on flow lines earlier. Here in the US, DOE has sponsored university tests where spheres were placed in plexiglass vessels to see how fueled and non-fueled pebbles would flow and used the information for computer code benchmarks. See:
A. C. Kadak and M. Z. Bazant, “Pebble flow experiments for pebble bed reactors,” in Proceedings of the 2nd International Topical Meeting on High Temperature Reactor Technology, pp. 22–24, Beijing, China, 2004. The slides are available at:
http://web.mit.edu/pebble-bed/papers1_files/Beijing%20pebble%20flow.pdf
The Chinese have also performed tests as well to benchmark computer simulations.
See: http://www.hindawi.com/journals/stni/2013/458190/
Please note that fuel interspersed into the coolant, e.g., ORNL's Molten Salt Reactor (1990's) is a proliferation hazard since weapons grade isotopes can be removed chemically from coolant. Modern Molten Salt Reactor designs (e.g. UC Berkeley and MIT) uses FIXED fuel elements and fuel-free molten salt.
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