The equation of state package FEOS for high energy density matter

Adequate equation of state (EOS) data is of high interest in the growing field of high energy density physics and especially essential for hydrodynamic simulation codes. The semi-analytical method used in the newly developed Frankfurt equation of state (FEOS) package provides an easy and fast access to the EOS of - in principle - arbitrary materials. The code is based on the well known QEOS model (More et al., 1988; Young and Corey, 1995) and is a further development of the MPQeos code (Kemp and Meyer-ter Vehn, 1988; Kemp and Meyer-ter Vehn, 1998) from Max-Planck-Institut fur Quantenoptik (MPQ) in Garching Germany. The list of features contains the calculation of homogeneous mixtures of chemical elements and the description of the liquid-vapor two-phase region with or without a Maxwell construction. Full flexibility of the package is assured by its structure: A program library provides the EOS with an interface designed for Fortran or C/C++ codes. Two additional software tools allow for the generation of EOS tables in different file output formats and for the calculation and visualization of isolines and Hugoniot shock adiabats. As an example the EOS of fused silica (SiO2) is calculated and compared to experimental data and other EOS codes. Program summary Program Title: FEOS Frankfurt equation of state P rogram Files doi: http://dx.doi.org/10.17632/6vjsv6v48p.1 Licensing provisions: GNU General Public License version 3 Programming language: C++ Supplementary material: Documentation/manual, exemplary input files for aluminum (Al)and fused silica (SiO2) Nature of problem: The description of a thermodynamic system e.g. by the solution of the hydrodynamic conservation equations presumes in the most cases reliable equation of state (EOS) data for different materials and for a wide range in temperature-density space. The FEOS code provides the required thermodynamic quantities like the pressure or the specific internal energy per unit mass as functions of density and temperature for, in principle, arbitrary materials, for single elements as well as for homogeneous mixtures of elements. FEOS is based on the well known QEOS model 121 and is a further development of the MPQeos code 111 from Max-Planck-Institut fur Quantenoptik in Garching. Since the model was designed for the high energy density matter regimes, it can be applied e.g. to high-power laser or ion beam and inertial fusion science applications. The most important advantage of the FEOS package is an easy and fast access to materials which may not be available by more complex EOS codes. Solution method: In the QEOS model the thermodynamic quantities are derived from the specific Helmholtz free energy f = is an element of- Ts, which is composed of three contributions f = f(e) + f(i) + f(b): (1) the uncorrected electronic part fe, calculated by a numerical scheme based on the simple Thomas-Fermi statistical model, (2) the ionic part fi, using the Cowan model [2], which employs analytical formulas to smoothly interpolate between the Debye solid, the normal solid and the liquid states, and (3) the semi empirical bonding correction fb, which is included to compensate for the negligence of bonding forces in the simple Thomas-Fermi model. Although the total EOS is calculated for a single temperature T = T-e = T-i, the user is free to calculate the ionic and the corrected electronic contributions independently with different temperatures. For homogeneous mixtures of elements the partial volumes of all element species k are iteratively adjusted in order to equilibrate the Thomas-Fermi pressures p(e,k) and to fulfill an additive volume rule for the electronic contribution. Furthermore, in the liquid-vapor two-phase region the model provides the (metastable) EOS with its characteristic features like van-der-Waals loops. The fully equilibrium EOS inside the two-phase region can be calculated by an iterative Maxwell construction scheme. Finally, despite the existence of the bonding correction, pressures near the critical point are often overestimated. Therefore, an improved cold curve can be applied to fit the location of the critical point to theoretical or experimental data. Additional comments: Besides the material's composition, the user must specify a reference density rho(0) and the bulk modulus K-0= rho(partial derivative p/partial derivative rho)(s) at a reference point (p, T) = (0, T-0) for a new material. The reference temperature T-0 is usually chosen such that at p = 0 the studied material is in the solid state. All fixed material parameters are stored in a material parameter database file which can be easily exchanged between users. The code is designed to calculate the equation of state within the following density and temperature limits: 10(-7) <= rho/rho(0) < 10(6),10(-4) eV <= T <= 10(6) eV. Homogeneous mixtures with more than three elements may implicate numerical difficulties and/or uneconomical computing times. For temperatures close to and below the critical point one must be careful to check the accuracy of the model. If available, a more complex EOS in this regime is preferable. The FEOS package was designed to provide the best possible flexibility and therefore consists of three parts: (1) the FEOS library which contains all the routines for the calculation of the EOS and which provides a C/C++ as well as a Fortran interface for this purpose, (2) the FEOS table generation tool which accesses the FEOS library in order to generate EOS table files (e.g. in the SESAME database [3] format), and (3) the SHOWEOS table visualization tool which was developed to provide isotherms, isochores, isentropes, and Hugoniot curves from the FEOS or SESAME tables. Application of the code was first demonstrated in a publication on liquid-vapor metastable states in volumetrically heated matter [4]. [1] A. J. Kemp, J. Meyer-ter Vehn, An equation of state code for hot dense matter, based on the QEOS description, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 415 (3) (1998) 674-676. doi:10.1016/S0168-9002(98)00446-X. [2] R. M. More, K. H. Warren, D. A. Young, G. B. Zimmerman, A new quotidian equation of state (QEOS) for hot dense matter, Physics of Fluids 31(1988) 3059. doi:10.1063/1.866963. [3] S. P. Lyon, J. D. Johnson, SESAME: The Los Alamos National Laboratory equation of state database, Tech. Rep. LA-UR-92-3407, Los Alamos National Laboratory (1992). [4] S. Faik, M. M. Basko, A. Tauschwitz, I. losilevskiy, J. A. Maruhn, Dynamics of volumetrically heated matter passing through the liquid-vapor metastable states, High Energy Density Physics 8 (4) (2012) 349-359. doi:10.1016/j.hedp.2012.08.003. (C) 2018 Elsevier B.V. All rights reserved.