Analytical solutions to shock and expansion waves for non-ideal equations of state

We present analytical solutions to the stationary normal shock and centered rarefaction waves, which are valid for arbitrary non-ideal equations of state (EOS). Generalized shock functions are defined, which are shown to be well-behaved and locally convex, facilitating rapid and exact computation of shock ratios. For rarefactions, a novel domain mapping is used to derive flow variables as closed-form analytical functions in space and time, independent of the EOS. Results are discussed for transcritical and supercritical CO2. The solutions enable researchers to test shock-capturing codes designed for non-ideal flows, and the derivation strategy opens possibilities to revisit nonlinear hyperbolic conservation problems that traditionally lack analytical solutions.