Abstract
An upwind finite-volume approximation scheme applicable to finite-element-type unstructured grids is proposed for the solution of steady, inviscid non-equilibrium flow when it can be assumed that the total specific enthalpy is constant throughout the entire domain. This is the case, in particular, for external non-radiating flows in which the freestream conditions are constant. In the present approach, the energy equation in differential form is replaced by its first integral which plays the role of a known algebraic constraint. The wellposeness of the restriction of the van Leer and Steger-Warming flux-vector splittings to this case is proved assuming the equivalent-γ can locally be treated as a constant. The efficiency of the proposed method is assessed by numerical experiments related to first-order and MUSCL-type second-order accurate solutions to hypersonic flow problems.
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