Capability Development for Modeling
Inclusive Dates: 06/18/01 - 10/18/01
Background - Solar system objects at Jupiter and beyond are ice-rich. Understanding collisional outcomes for such compositions is central to models of the origin and evolution of systems such as the Pluto-Charon binary system and the large icy satellites of the giant planets. Impacts by ice-rich objects are believed to be a potential delivery mechanism for supplying Earth with its initial water budget. In this project, the team received support to develop the capability to simulate collisions between planet-scale (greater than 1,000 kilometers) objects that contain water ice. Previously, SwRI lacked this ability because the equation of state utilized in the smooth particle hydrodynamics (SPH) code, while quite good for rock objects, was inadequate to model the behavior of ice upon compression and yielded highly erroneous and unphysical results in this case. The research team addressed this key deficiency by incorporating a recently developed version of the sophisticated equation of state (EOS) known as ANEOS (Thompson and Lauson, 1972; Melosh, 2000) into the existing SPH code.
Approach - SPH offers a tremendous advantage for solving certain kinds of problems, particularly those in which matter undergoes intense deformation and mixing, and where a Lagrangian formalism is desired for keeping track of compositions. In SPH, objects are represented by spherical overlapping 'particles' whose evolution is tracked as a function of time. For planet-scale impacts of interest here, the evolution of each particle's kinematic (position and velocity) and state (internal energy, density) variables are evolved due to 1) gravity, 2) compressional heating and expansional cooling, and 3) shock dissipation.
Previously, SwRI utilized the Tillotson EOS (Tillotson, 1962), a relatively simple EOS that is compact and analytical. The weakness of Tillotson lies in its lack of detailed phase transitions, being characterized by a condensed regime and a vapor regime, but no true liquid. Tillotson does not properly treat mixed phases, instead simply deriving the pressure in energy regimes intermediate to those of a condensed solid and an expanded gas by interpolation; thus, phase transitions are not treated in a thermodynamically consistent manner.
The team's strategy is to incorporate ANEOS into SwRI's SPH code. In ANEOS, different phases are treated as separate components that are in temperature and pressure equilibrium; quantities in all states are derived from the Helmholtz free energy, yielding a thermodynamically consistent set of state variables at all times. The standard version of ANEOS treats all vapor as monatomic species, so that the energy and entropy required for vaporization is overestimated for molecular vapors, such as water vapor. Here SwRI incorporated a recently completed extension to ANEOS to accommodate the formation of molecular vapor species (Melosh, 2000).
Accomplishments - The team successfully incorporated the ANEOS package into the SPH code; this addition involved added subroutines totaling more than 8,000 lines of FORTRAN code. Material constant files were included for ANEOS for five substances of interest to SwRI's planetary impact problems: water, ice, serpentine, dunite, and iron. The team has completed multiple test impact simulations with the new ANEOS, and find that collisions involving ice and ice-rock mixes are now well behaved. In addition, the use of ANEOS instead of the much simpler Tillotson EOS has not drastically affected the computational speed of calculations. Below is a sample simulation using SPH with ANEOS to model the impact of two 1025 gram ice objects. Such an impact could not be modeled previously with SPH using the Tillotson EOS.