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A novel ES-BGK-based model of non-polytropic rarefied gases in the frameworkof kinetic theory is presented. Key features of this model are: an internalstate density function depending only on the microscopic energy of internalmodes (avoiding the dependence on temperature seen in previous referencestudies); full compliance with the H-theorem; feasibility of the closure of thesystem of moment equations based on the maximum entropy principle, followingthe well-established procedure of Rational Extended Thermodynamics.  The structure of planar shock waves in carbon dioxide (CO$_2$) obtained withthe present model is in general good agreement with that of previous results,except for the computed internal temperature profile, which is qualitativelydifferent with respect to the results obtained in previous studies, showinghere a consistently monotonous behavior across the shock structure, rather thanthe non monotonous behavior previously found.

A Novel ES-BGK Model for Non-Polytropic Gases with Internal State Density Independent of the Temperature