Equation of state for continuously varying mixtures

Determine a consistent and accurate equation-of-state modeling strategy for continuously varying mixtures in continuum hydrodynamic simulations, specifying how pressure, density, and internal energy should be defined and updated when mixture composition varies continuously in space and time.

Background

The paper introduces a concurrent continuum–atomistic framework that bypasses traditional equations of state (EOS) by invoking molecular dynamics at quadrature points in a finite-element hydrodynamics code. While the approach demonstrates accuracy and computational feasibility for metals under shock and for deuterium at high pressures, the authors highlight that EOS modeling challenges persist for cases where material composition varies continuously, such as mixtures.

In the conclusion, the authors explicitly note the lack of consensus on how to treat the EOS for continuously varying mixtures, underscoring a key unresolved issue in hydrodynamic material modeling. Addressing this would enable more reliable simulations in applications where mixture composition evolves dynamically and cannot be captured by simple tabular or analytical EOS formulations.