An HLLC-type Riemann solver and high-resolution Godunov method for a two-phase model of reactive flow with general equations of state

Abstract

A high-resolution Godunov method is developed for a two-phase model of reactive flow. The model considers general equations of state of Mie-Grüneisen form and different choices for the reaction rate, both relevant for simulations of the dynamical behavior of detonations in PBX-type granular explosives. The numerical approach employs a Riemann solver, and various options ranging from an exact solver to an approximate solver of HLLC type are described. A principal aim of the paper is an assessment of the approximate Riemann solvers in terms of the accuracy and efficiency of numerical solutions of the two-phase model. In particular, this study considers the state-sensitive behavior in different regimes of the solutions in a reverse-impact configuration, including compaction, run to detonation, and the evolution to compaction-led and reaction-led steady detonations. For these regimes, the convergence properties of the numerical approach are examined for the different choices of the Riemann solver, as is the error in the solutions at lower grid resolution. Finally, the computational performance of the time-stepping scheme is assessed for the different solvers.