Hydro-Code Implementation and Testing of a Kinetic Phase Transition Framework

Abstract

In this report we describe the Kinetic Phase Transition (KPT) framework that has been worked out over the last 10 years (from around 2014) and the implementation of it into three different codes, the one-dimensional hydro- LASLO and the three-dimensional magneto-hydro- ALEGRA, Sandia codes, via subroutines in the LAMBDA Equations of State and constitutive models package, and Flag, an arbitrary Lagrangian-Eulerian multiphysics code developed within the Lagrangian Applications project (LAP) at LANL. We discuss the introduction of phase mass (and/or volume) fractions that are needed in a code for it to be ‘phase aware’, that is, not only the thermodynamic state is known in each point but also the mixture of the materials’ phases in that point. Further we point to the need of a full Equations of State for each phase in a material to achieve phase awareness and we review the equilibrium phase model, where a phase mixture is at its lowest Gibbs free energy state, to make this point clear. Contrasting the kinetic phase transition to this equilibrium model seamlessly introduce us to the KPT framework that is subsequently thoroughly discussed. While the determination of the total state and the states and mass fractions of phases in each point is a problem that can borrow many of its numerical details from Eulerian codes and mixture of materials (not phases), the update of mass fractions with time in a KPT framework needs a new set of considerations. General for any update model is that we need to prevent mass fractions from becoming unphysical (negative or their sum to be larger than one). We have solved this problem by implementing a subdivision of the hydro time step that prevents the phase from being fully present to not present at all in one subdivided time step by limiting the size of the subdivided time step. This scheme also corrects numerical problems from abrupt changes in parameter values, the so called Gibbs phenomena, that gives rise to slushing between phases in the KPT framework. Interspersed throughout the report are discussions on different thermodynamics considerations. EOS validity windows, limitations on the EOS phase space, are needed for the KPT framework and are discussed separately and exemplified. The KPT framework described in this report has been verified by code comparison, but validation is still an active area of research. There is room for improvement in the update model, both in the model for determination of rates and in how to prevent the mass fractions from becoming unphysical. In addition, the parameters in the KPT update model and the placement of the phase boundary in the EOS phase space, and interactions with other constitutive models, are closely related and interfering with each other. One possible way forward is to simultaneously develop KPT parameters, EOS, and constitutive models for each material.