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Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.
The Accuracy, Consistency, and Speed of Five Equations of State for Stellar Hydrodynamics

In this paper, we compare the thermodynamic properties and execution speed of five independent equations of state. A wide range of temperatures, densities, and compositions are considerebdconditions appropriate for modeling the collapse of a cloud of hydrogen gas (or an exploding supernova) to the outer layers of a neutron star. The pressures and specific thermal energies calculated by each equation-of-state routine are reasonably accurate (typically 0.1% error or less) and agree remarkably well with each other, despite the different approaches and approximations used in each routine. The derivatives of the pressure and specific thermal energies with respect to the temperature and density generally show less accuracy (typically 1% error or less) and more disagreement with one another. Thermodynamic consistency, as measured by deviations from the appropriate Maxwell relations, shows that the Timmes equation of state and the Nadyozhin equation of state achieve thermodynamic consistency to a high degree of precision. The execution speed of the five equation-of-state routinebsevaluated across several different machine architectures, compiler options, and modes of operatiobndiffer dramatically. The Arnett equation of state is the fastest of the five routines, with the Nadyozhin equation of state close behind.

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Pressure
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Pressure differences
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Thermodynamic consistency


The Accuracy, Consistency, and Speed Of An Electron–Positron Equation Of State
Based On Table Interpolation Of The Helmholtz Free Energy

In this paper, an electron-positron equation of state based on table interpolation of the Helmholtz free energy is developed and analyzed. The interpolation scheme guarantees perfect thermodynamic consistency, independent of the interpolating function. The choice of a biquintic Hermite polynomial as the interpolating function results in accurately reproducing the underlying Helmholtz free energy data in the table, and yields derivatives of the pressure, specific entropy and specific internal energy which are smooth and continuous. The execution speed – evaluated across several different machine architectures, compiler options, and mode of operation – suggest that the Helmholtz equation of state routine is faster than any of the five equation of state routines surveyed by Timmes & Arnett (1999). When an optimal balance of accuracy, thermodynamic consistency, and speed is desirable, then the tabular Helmholtz equation of state is an excellent choice, particularly for multidimensional models of stellar phenomena.

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Pressure
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Specific internal energy
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Entropy


Equation of State Codes
Open-source codes are avaliable from this link and this link