Derivation of a Numerical Method for Computing 3-D Magnetoplasmadynamic Flows in Thermodynamic Non-equilibrium

Various models exist for the propulsion concept using magnetohydrodynamics (MHD). Various authors, such as Powell, Canupp, Candler, and MacCormack have dealt with issues of solving the magnetic field induction equations simultaneously with Navier-Stokes equations using Computational Fluid Dynamics (CFD). Although most authors deal with species non-equilibrium and thermal non-equilibrium, a new emphasis is set to study the impact of electrons with the electron energy and the electronic excitation energy, as well as a complex energy non-equilibrium. This thesis presents the derivation of a numerical method for computing 3-D MHD flows for the purpose of modeling steady-state magnetoplasmadynamic thrusters (MPDT). It details the derivations of each equation: both Navier-Stokes and the induction equation when the magnetic term is treated as a body force and the electron pressure as a surface force. The method of flux vector splitting has been chosen to solve the set of ns+12 equations, ns being the number of heavy particles involved in the flow. In addition, it presents the mathematical issues encountered in using this method. The first part of the method has been solved, finding the conserved variables, flux vectors, flux vector Jacobian, and eigenvalues