  In this article we present a new formulation and an associated algorithm for
the simultaneous numerical simulation of multiple condensed phase explosives in
direct contact with each other, which may also be confined by (or interacting
with one or more) compliant inert materials. Examples include composite
rate-stick problems and interaction of shock waves with chemically-active
particles in condensed-phase explosives. There are several formulations which
address the compliant or structural response of confiners and particles due to
detonations, but the direct interaction of explosives remains a challenge for
most formulations and algorithms. The proposed formulation addresses this
problem by extending the conservation laws and mixture rules of an existing
hybrid formulation to model the interaction of multiple explosive mixtures. An
algorithm for the solution of the resulting system of partial differential
equations is presented, which includes a new robust method for the retrieval of
the densities of the constituents of each explosive mixture. The algorithm is
implemented in a hierarchical adaptive mesh refinement framework and validated
against results from problems with known solutions. It is evaluated for
robustness for rate-stick and shock-induced flows in particle-laden explosives
case-studies. It is shown that the method can simulate the interaction of
detonation waves produced by military grade and commercial explosives in direct
contact, each with its own distinct equation of state and reaction rate law.
The ability of the new model to simulate reactive particles which are
explicitly resolved in a heterogeneous explosive is demonstrated by a
case-study of a shock wave interacting with a high explosive bead embedded in
liquid nitromethane.
