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Computational plasma physics is concerned primarily with the study of the evolution of plasma by means of computer simulation. The main task of this computational branch is to develop methods able to obtain a better understanding of plasma physics. Therefore a close contact to theoretical plasma physics and numerical methods is necessary. Ideally computational plasma physics acts as a pathfinder to guide scientific and technical development and to connect experiment and theory. To build a valid computer simulation program means to devise a model which is sufficiently detailed to reproduce faithfully the most important physical effects, with a computational effort sustainable by modern computers in reasonable time (Dandy, 1993). Computational models have played an important role in the development of plasma physics since the beginning of the computer age. Advances in our understanding of many plasma phenomena like magnetohydrodynamic instabilities, micro-instabilities, transport, wave propagation, etc. have gone hand-in-hand with the increased computational power available to researchers. Several trends are evident in how computer modelling is carried out: the models are becoming increasingly complex, for example, by coupling separate computer codes together. This allows for more realistic modelling of the plasma. Presently several efforts are carried out in different countries to develop plasma numerical tools for several applications such as fusion, electric propulsion, active control over hypersonic vehicles: these efforts lead to a growing experience in CMFD field (see Park et al. 1999, Kenneth et al 1998, Taku and Atsushi 2004, Cristofolini et al 2007, Miura and Groth 2007, MacCormack 2007, Yalim 2001, Giordano and D’Ambrosio 2004, Battista 2009). The chapter presented was carried out in the context of a research activity motivated by renewed interest in investigating the influence that electromagnetic fields can exert on the thermal and pressure loads imposed on a body invested by a high energetic flow. In this regard, spacecraft thermal protection and the opportunity to use active control surfaces during planetary (re)entry represent the driving engineering applications. The contents of the study should be considered, to a certain extent, a systematic re-examination of past work complemented with somewhat innovative ideas. So, in this chapter, methodologies for plasma modelling have been developed and then implemented and tested into a numerical code EMC3NS, developed in the frame of this

A Magneto-Fluid-Dynamic Model and Computational Solving Methodologies for Aerospace Applications