A NUMERICAL STUDY OF INTERFACIAL INSTABILITIES IN SHOCKED MATERIALS WITH SURFACE TENSION
Shock-driven multi-material flows occur in several applications including shock wave lithotripsy, underwater explosions, droplet combustion, propeller cavitation and ejection of material from surfaces subject to blast loading. Such flows are highly compressible due to the presence of strong shocks, yet are influenced to a significant extent by surface tension forces at the interface separating two or more materials. In particular, surface tension can impact the evolution of the interface, by stabilizing hydrodynamic instabilities occurring at the interface. The presence of surface tension can also influence aspects of the late-time interface breakup process, and determine the size distribution, transport, subsequent breakup and phase change of droplets. The modeling of such flows requires the development and application of specialized numerical methods, capable of handling the multi-physics nature of the flow dynamics. In this work, we report on the development and validation of novel numerical methods for shock-driven multi-material flows with surface tension. The numerical methods have been implemented in IMPACT, a Computational Fluid Dynamics software, with a wide array of physics capabilities including compressible flows with multiple equations of state, surface tension, and phase change. IMPACT solves the Euler equations using a finite volume approach, and exploits the Roe Riemann solver to obtain intecell fluxes. A fifth-order WENO reconstruction for spatial discretization is coupled with a third-order TVD Runge-Kutta scheme for time discretization. The Level Set method is implemented in IMPACT to track the interface between materials and to obtain interface curvature required for surface tension calculations. Interfacial boundary conditions are applied to the cells bordering the material interface using the Ghost Fluid Method (GFM). In the presence of surface tension, the GFM is modified to account for the pressure jump across the curved interface stemming from surface tension effects. The GFM and its variants have been used extensively in the numerical treatment of shocked, multi-material flows, but are susceptible to overheating errors near the interface as well as spurious numerical reflections. To address these issues, we have developed a novel, highly accurate variation of the GFM called the Efficient GFM (EGFM) which removes overheating errors at the interfaces and numerical reflections, resulting in numerical solutions that are in agreement with analytical solutions. When compared with the original GFM approach and its subsequent variants, the EGFM scheme proposed here is robust, and has been demonstrated in this dissertation to accurately simulate a wide range of Riemann problems and shock-interface problems.