Non-Equilibrium Hypersonic flow Computations by Implicit Second-Order Upwind Finite-Elements
Second-order implicit schemes are constructed for the solution of steady hypersonic chemically-reacting inviscid flows. In a standard non-equilibrium model accounting for 5 species (N2, O2, NO, N and O), the Euler equations are coupled with species convection equations. In a fractional-step approach, the set of fluid motion equations and the set of chemical kinetics equations are alternatively time-marched, both sets implicitly. The basic approximation method employs a finite-volume formulation applicable to arbitrary Finite-Element-type unstructured triangulations. The accuracy is enhanced by the M.U.S.C.L. extrapolation, and quasi-second-order solutions are obtained by slope-limitation or TVD-averaging. The merits of the various proposed approximations are evaluated by numerical experiments, computing the hypersonic flows over a cylinder and around a model geometry for the HERMES space shuttle.
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