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Chapter 5 Conclusions This thesis presents an HDG formulation and numerical scheme for solving the EHD thruster governing equations. The approach is used with a model problem, a single stage thruster geometry, and a dual stage thruster geometry to assess solution accuracy and performance. The validation analysis shows that the scheme accurately solves the governing equations and replicates test results when using a posteriori charge injection boundary conditions. A predictive charge injection boundary condition poses numerical challenges which require more computing resources to improve accuracy. The HDG scheme implemented here successfully solves the governing equations within a normalized error on the order of 10' for second order elements. Further, the solution is achieved with less than 10 Newton iterations. The number of solution iterations is reduced if the initial solution is close to the final solution. The convergence rate for the potential solution is better than second order and variable with each iteration. The convergence rate for the charge density can be as good as second order. The ideal charge injection boundary condition was not implemented since it always allows the trivial solution. The CG-FEM implementation by Feng [13] required additional residual equations to avoid this problem. The charge injection boundary condition model proposed by Cagnoni et al. [4] is used instead. The model does not allow the trivial solution and is tunable to balance stability and accuracy via the 75