This report presents a numerical model to simulate the electromagnetic processes involved by electrically-charged relativistic fluids. The physical model is first given. Second, the numerical methods are explained with the various packages of the code RHEA, with indication of their performances, within a 1.5-dimensional framework. Results from test-simulations are shown to validate the use of the code, for both academic situations and realistic context of laser-plasma interaction, for which the code has been designed: the non-linear phenomena in the context of inertial confinement fusion and the ultra-intense laser pulses.

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