Methods that are capable of Enhanced Discretization to a basic formulation have been proposed for improved accuracy. A new formulation that is applicable to all regimes of Mach numbers has been proposed and tested. Various definitions of {\it element length} have been investigated and the one that results in the best results has been identified. Various preconditioners, that improve the convergence of the iterative solvers for the equation systems resulting from finite element discretization of the governing equations, have been tested. Parallel processing has been employed to speed up the computations.
 
 

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