Adaptive moving window technique for SPH simulation of stationary shock waves

Abstract

A novel adaptive moving window (AMW) technique is developed for simulating stationary shock waves in a moving coordinate system associated with a simulation box. The velocity of this system is adjusted by an iterative feedback algorithm with the purpose of establishing a desirable position of shock front. Galilean transformations are iteratively used to maintain the shape of the flow profile. The moving coordinate system has advantages in simulation over a conventional coordinate system associated with the intact material at rest. In particular, a truly steady flow regime can be established in this moving window (MW). Comparative simulation using the smoothed particle hydrodynamics method to study shock propagation in copper confirms that the AMW converges to a steady state faster than a MW technique with a fixed velocity. We demonstrate that AMW can be applied for very weak shocks. Advantage of AMW is revealed in SPH simulation of the front structure for weak shocks in porous copper that result in a partial pore compaction. Specifically, we clarify the mechanism of the partial pore collapse for shock velocities below a knee on a calculated shock Hugoniot, where this knee corresponds to the complete collapse of pores.