Verifying the working principle of a magnetic flux compression reaction chamber might be crucial for the development of pulsed fusion propulsion: a system that has been projected to possibly revolutionise manned space exploration. For that purpose, an exhaustive computational MHD analysis is a necessary step. This master thesis investigated the possibility of using PLUTO to estimate the ideal-MHD of a multi-coil parabolic reaction chamber. PLUTO is a freely-distributed and modular code for computational astrophysics that, although not originally programmed for engineering applications, has demonstrated great adaptation capabilities: implementing the boundary conditions to effectively emulate a magnetic flux compression reaction chamber has eventually been possible. Besides, the attained results are in accordance with theoretical projections and previous numerical analyses. However, the outcomes pointed out that ideal-MHD could be an over-simplified model: relativistic conditions, that are not properly reproduced by the ideal-MHD equations, have been identified in several locations of the computational domain. In addition, some aspects of the real system physics have yet to be thoroughly investigated as well as mathematically described. Therefore, further investigations are required. According to this research, no other computational analyses of a multi-coil parabolic reaction chamber (i.e. the latest and most promising magnetic flux compression reaction chamber concept) have been found in the literature. Therefore, the results hereby reported contribute to the body of knowledge of plasma physics and nuclear fusion applied to space propulsion.