Adaptive HP-refinement of Detonation Waves Interacting with Voids in Energetic Materials*

Computational modeling of detonations in energetic materials is used to gain insight into the processes that occur when a high explosive is detonated. The ZND model proposes that this phenomenon consists of an infinitesimally thin shock which compresses the explosive to a high pressure, the Von Neuman spike. Behind the Von Neuman spike is an exothermic chemical reaction zone in which the pressure decreases smoothly to the Chapman - Jouguet condition. Capturing both the discontinuous spike and the continuous pressure decrease can be computationally challenging and expensive. When 2D features, such as a void region within the energetic material, are introduced they lead to more features that need to be resolved such as a re-initiation zone. To accurately capture all of these events, an adaptive hp-refinement strategy is used. In regions of discontinuities, an element is kept at a low polynomial order but is split into smaller children elements (h-refinement). This increases the resolution of the discontinuity while avoiding spurious oscillations that may occur. In other regions, the polynomial order within an element is increased but is not split into smaller children elements (p-refinement). The increased polynomial order leads to a more resolved solution without memory storage cost incurred during h-refinement. By combining these two strategies, all flow features can be accurately captured while being computationally inexpensive.