Conservation-variable average states for the multi-dimensional Euler fluxes and arbitrary equilibrium real gases

This paper focuses on the development of an equilibrium real-gas Riemann solver that requires no auxiliary assumptions for computing the average pressure derivatives to determine the multidimensional average flux-vector Jacobian. By employing the multidimensional mean value theorem, the theoretical developments give one average pressure and two internal conservation-variable average states that correspond to intermediate states between the given right and left states. These states are utilized to compute the average sound speed and pressure derivatives without any additional internal energy, geometric projections, and scale factors.