Mixture-conservative temperature-based Baer–Nunziato solver for efficient full-disequilibrium simulations of real fluids

In this work, we present a primitive update scheme for the full-disequilibrium Baer–Nunziato equations that is conservative in the total energy of the mixture and valid for generic equations of state. The update scheme is derived for a generic thermodynamic variable and is independent of the chosen spatial discretization. We show results of various Riemann problems from the literature obtained by updating phasic temperatures through the proposed scheme and compare them to the standard approach and analytical solutions. The total energy imbalance of the mixture is assessed, and computational speed-ups using the Span–Wagner equation of state are briefly discussed. Finally, the scheme is tested in complex thermodynamic conditions on a two-phase non-ideal and a two-fluid non-classical Riemann problem, using the Span–Wagner equation of state with vanishing phases.