Abstract
We present a method for constructing a thermodynamically consistent bi-quintic interpolation scheme that permits the construction of accurate equation of state (EOS) tables. Thermodynamic consistency requires that the first law of thermodynamics be satisfied exactly, i.e., that the pressure and entropy must satisfy the appropriate Maxwell relations. Furthermore, the pressure and internal energy must satisfy their definitions in terms of the derivatives of the Helmholtz free energy. We delineate in this paper a method of high-order interpolation in tables of the Helmholtz free energy, and its derivatives with respect to density and temperature, that ensures that both of these consistency conditions are exactly satisfied. This technique is capable of building highly accurate and consistent EOS tables as a function of temperature and density for use in numerical simulations of reactive flows where the maintenance of thermodynamic consistency is critical. In addition, this method of interpolation maintains continuity of the derivatives of pressure and internal energy with respect to density and temperature. This formalism can be extended to the case where the EOS is a function of chemical composition variables as well as density and temperature.
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