High-order schemes for simulation of shock-interface interactions in micro-structured materials

The response of materials to high strain rate loading is important in applications such as high-speed impact and penetration, high speed flows with particles and shocked flows in multi-material media. For example, the thermomechanical response of energetic materials (EMs) to shock loading is used to characterize their sensitivity. The initiation of EMs depends on shock interactions with their complex microstructure (void spaces/defects and crystal-crystal interfaces). Previous studies have employed at best 3rd-order accurate numerical schemes for shock simulations in EMs, requiring well-resolved simulations to obtain grid-independent solutions. High-order accurate methods can provide an improved balance between computational time and accuracy of calculations. Here, a non-characteristic 5th-order WENO scheme is used to study the response of materials with complex internal structure under shock loading using an Eulerian framework. The high-order scheme is combined with levelsets to define interfaces and a HLLC (Harten,-Lax-van Leer-Contact) approximate Riemann solver is employed to eliminate numerical oscillations and maintain high-order reconstruction across the sharp interface. Test problems involving high speed impact, shocks, elastic-plastic flows and interfaces are used to evaluate the accuracy, computational cost, and performance of the high-order methods. The new techniques provide unprecedented resolution of both embedded interfaces and their dynamics, as well as resolution of shock systems and reaction fronts.