Relativity with Charged Particles & Fluid Approx.

[qqqppp]

Hello community, I'm new here.

I'm using FORTRAN to model the motion of electrons and ions when accelerated under a high voltage potential. I'm using a fluid approximation and MHD-like equations (conservation of mass, energy, momentum) and a finite volumes numerical method to solve the equations.
The thing is that when the electron density is high, the particles' speed exceed the speed of light. I thought that replacing m with γm would fix the problem, at least as a first-order approximation, but it didn't. I'm afraid I need to replace everything with its corresponding 4-vector but this requires a complete rewrite of the program from start.

Any ideas?

 

[Markus Hanke]

If you wish to fully account for relativistic effects, you will have no choice but to use the relativistic version of the MHD equations; this automatically brings you into the realm of 4-vectors and Minkowski tensors. No way around this, I'm afraid.