Development of an inviscid flux scheme for thermochemical nonequilibrium flow

Solutions to the governing equations that model hypersonic aerothermodynamics rely heavily on the mathematical and numerical technology that characterizes Computational Fluid Dynamics. Many areas of significant investigation are relevant to advancing state of the art hypersonic aerothermodynamic engineering and applied research analyses. Due to the relatively high energy achieved by spacecraft during launch, physical models for thermal nonequilibrium and chemical nonequilibrium are necessary to develop adequate numerical reentry simulations. In addition, complex features of the Navier Stokes equations require sophisticated mathematical and numerical techniques in order to develop reasonably accurate simulations in an acceptable amount of time. The objective of this work is to present the development of a new inviscid flux evaluation method. This new method, referred to as the Flux Consistent scheme, is closely related to the Modified Steger-Warming method. The unique characteristics of this new flux scheme involve an original eigenvalue implementation. This original eigenvalue formulation, however, leads to incorrect flux magnitudes which must be corrected in the total flux to provide an accurate representation of the inviscid fluxes. The mathematical technique used to identify flux magnitude errors in the Flux Consistent scheme is also applied to the Modified Steger-Warming flux evaluation method. This assessment leads to the characterization of flux errors in the Modified Steger-Warming scheme which are generated by eigenvalue differences between the left and right cell interface flow states. These Modified Steger-Warming flux errors are shown to vanish for supersonic conditions. Two hypotheses in reference to the Modified Steger-Warming scheme are proposed. The first is that sonic glitch problems occurring in some Steger-Warming simulations are the result of the flux error vanishing at supersonic conditions. The second hypothesis concerning the Steger-Warming method is that stagnation region carbuncles are generated as a result of the flux errors identified in this work. Both of these hypothesis remain open for consideration, and are not validated in this thesis. Axisymmetric numerical simulations for a sphere at hypersonic reentry conditions are assessed for implementations of the Modified Steger-Warming and Flux Consistent inviscid flux schemes.