Computational Modeling of Energy Deposition in Solids
Energy deposition techniques such as Pulsed-power mining technologies use intense pressure waves to fracture submerged ore and rock. Water plays an active role in this process: pressure waves propagate through the fluid and reflect at solid–water interfaces, while cavitation and the subsequent collapse of vapor cavities can generate localized tensile loading and water-hammer effects. At the same time, the surrounding water damps fragment motion and alters the transfer of energy into the rock. These coupled phenomena create opportunities to control and enhance fragmentation, but they also make pulse and device designs difficult to predict. Since existing open computational tools do not yet provide an integrated treatment of the fluid, cavitation, the ability to consider strength as a parameter, and solid-failure mechanisms needed for this problem, the development relies heavily on costly experiments and iterative prototyping.
In this project, we are developing a predictive computational framework within the FLASH code to simulate the propagation, focusing, and reflection of acoustic waves and shocks in water. FLASH is an open, parallel, multiphysics simulation code with adaptive mesh refinement and established capabilities for modeling shocks, high-energy-density physics, and pulsed-power systems. We will use these capabilities to design shaped water containers that direct pressure waves toward submerged rock and to quantify the resulting pressure, impulse, and energy-density distributions. The simulations will enable us to evaluate container geometries and pulse characteristics over a much larger design space than can be explored experimentally.
A central technical contribution of the project is the introduction of tensile-pressure and cavitation capabilities into FLASH. Conventional hydrodynamic formulations are generally designed for compressive states and cannot adequately represent the large tensile regions and vapor cavities produced after strong pressure-wave reflections. We will address this limitation through a staged modeling strategy. The initial model will extend the water equation of state into the tensile regime and impose a physically motivated pressure cutoff at the vapor threshold. When the local pressure reaches this threshold, a portion of the liquid will be converted into a low-density vapor phase while conserving mass and energy. FLASH’s volume-of-fluid method will then track the evolution, transport, interaction, and collapse of the resulting cavitation regions.
A subsequent extension will incorporate surface-tension effects through curvature-dependent interfacial stresses. This higher-fidelity formulation will improve predictions of bubble shape, collapse, and jet formation, particularly in regimes where capillary effects become important. The staged approach provides an immediately useful model for large cavitation zones under strong loading while establishing a pathway toward more detailed simulations of bubble-wall dynamics. One of the parallel longer-term visions for this project is to incorporate equations of state in the solver to develop capabilities in modeling hyper-velocity planetary impacts.