Comsol is relatively popular for these sorts of complex models, and it has a plasma and fluid dynamics module. However, it is expensive (>£2000 I think) and in some respects, quite limited in its functionality. 

I think your model will be very complex. Will you be including electrohydrodynamic effects from the plasma? Is your model for chemical reactions, or flow stabilisation? 

I believe that the leadings groups for plasma modelling are that of Annemie Bogaerts (Antwerp - Plasmant) and Mark Kushner (Michigan). Perhaps try reading some of their publications for some insight?

Agree with Tom. COMSOL has its discount for college.

Thanks for your suggestion

I have flow with a High Reynolds and I don't know if turbulence models in Comsol can resolve well this kind of flow.

I have seen on the internet a Plasimo and VizGlow software. Anyone has an experience with this software

Don't expect to find a "out of the box" software for your problem if you are doing research (and not just technical applications). With a problem as complex as you mention (DBD, chemistry, turbulent flow) probably the solution lies on a mix of codes that you should adapt to the problem. In low-temperature plasma simulation groups that have developed software are Mark Kushner, the Plasimo group, The Lisbon group also has a multi-physics code "Spark" (contact through [email protected]) focus on plasma modelling. For the flow part and multi-physics problems look for Elmerfem from the Finish CFC. You will also need an electron Boltzmann equation solver.

Multi-physics codes can be adapted to this sort of problem. However, for a simpler (older look at the problem), look at "Experimental and CFD Studies of Non-Thermal Plasmas for NOx Control," Nusca et al 1998. Itn is attached here. However, the author Miziolek has retired and I don't know about the rest,

https://www.comsol.com/model/dielectric-barrier-discharge-8637

Comsol, if you already have it, check if there is a plasma module, otherwise, you may need to purchase it. wish you success.

If you tend to get exact results with high speed calculations for far many cells domain, Fortran and C++ will be excellent candidates.