tions to correctly describe the behavior of matter. Obviously many of these approaches are highly impractical for
We present a method for constructing a thermodynamically consistent bi-quintic interpolation scheme that permits the construction use in the course of a radiation-hydrodynamic simulation of accurate equation of state (EOS) tables. Thermodynamic consisbecause the numerical evaluation of such complex equatency requires that the first law of thermodynamics be satisfied tions of state are computationally prohibitive. In some exactly, i.e., that the pressure and entropy must satisfy the approcases, such as lattice simulations or in molecular dynamics priate Maxwell relations. Furthermore, the pressure and internal simulations, the evaluation of the internal energy and presenergy must satisfy their definitions in terms of the derivatives of the Helmholtz free energy. We delineate in this paper a method of sure at a single density and temperature may require more high-order interpolation in tables of the Helmholtz free energy, and computational effort than an entire radiation hydrodyits derivatives with respect to density and temperature, that ensures namic simulation.
that both of these consistency conditions are exactly satisfied. This
In addition to calculational difficulties, the EOS may technique is capable of building highly accurate and consistent EOS exhibit a wide range of behavior over the range of temperatables as a function of temperature and density for use in numerical simulations of reactive flows where the maintenance of thermody-ture and density that one is interested in. Such behavior namic consistency is critical. In addition, this method of interpolamay manifest itself as sharp discontinuities in thermodytion maintains continuity of the derivatives of pressure and internal namic variables near phase transitions and coexistence energy with respect to density and temperature. This formalism can boundaries. When the EOS is based on theory it may rely be extended to the case where the EOS is a function of chemical on different underlying physical models or calculational composition variables as well as density and temperature. แฎ 1996 Academic Press, Inc.
techniques in different ranges of temperature and density. This is particularly true for multi-phase chemical equilibrium models for the EOS, such as liquid drop models for 118