A Godunov-type method for the seven-equation model of compressible two-phase flow

We are interested in the numerical approximation of the solutions of the compressible seven-equation two-phase flow model. We propose a numerical srategy based on the derivation of a simple, accurate and explicit approximate Riemann solver. The source terms associated with the external forces and the drag force are included in the definition of the Riemann problem, and thus receive an upwind treatment. The objective is to try to preserve, at the numerical level, the asymptotic property of the solutions of the model to behave like the solutions of a drift-flux model with an algebraic closure law when the source terms are stiff. Numerical simulations and comparisons with other strategies are proposed

A Positive and Entropy-Satisfying Finite Volume Scheme for the Baer-Nunziato Model

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Toro-Tokareva's HLLC scheme [42]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions

A Multi-Scale Approach for Modeling Shock Ignition and Burn of Granular HMX

Deflagration-to-detonation transition (DDT) in confined, low-density granular HMX (65%-85% Theoretical Maximum Density, TMD) occurs by a complex mechanism that involves compaction shock interactions within the material. Piston driven DDT experiments indicate that detonation is abruptly triggered by the interaction of a strong burn-supported secondary shock and a piston-supported primary (input) shock, where the nature of the interaction depends on initial packing density and primary shock strength. These interactions influence transition by affecting hot-spot formation within the micro-structure during pore collapse. In this study, meso-scale simulations of hot-spot formation in shock loaded granular HMX are used to guide the development of a new hot-spot based macro-scale ignition and burn (I&B) model. The model is conceptually similar to conventional I&B models but describes ignition in terms of pressure-dependent hot-spot formation rate and describes burn in terms of a dissipation-dependent regression rate that accounts for the onset of hot-spot facilitated burn for sufficiently strong shocks. Inert macro- and averaged meso-scale predictions show good agreement, provided that the averaging area size is suitably selected. The I&B model reasonably predicts features representative of a Type-I DDT mechanism that is typical of particulate beds. The mechanism involves the formation of a solid-plug (i.e., a region having 100% TMD) within the bed that significantly affects reaction provided that the local dissipated work is insufficient to trigger hot-spot facilitated burn. Hence, the solid-plug affects the wave dynamics associated with transition. The model also predicts features characteristic of ignition and burn-controlled transition mechanisms and reasonably predicts time and distance to detonation over a wide range of piston impact speeds (150-600 m/s) and initial packing densities (68%-83% TMD). The shock strength required for transition from ignition to burn-controlled initiation increases with initial packing density, and is estimated to be approximately 0.2, 0.32, and 0.39 GPa for \phi_0= 0.68, 0.77 and 0.83, respectively. Predictions also highlight conditions favorable for the formation of spontaneous combustion waves whose propagation speed is influenced by shallow spatial gradients in solid volume fraction within the plug region

ICASE

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in the areas of (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving Langley facilities and scientists; and (4) computer science