Ghost Fluid Method for Strong Shock Interactions Part 1: Fluid-Fluid Interfaces

The interaction of shocks with multimaterial interfaces can occur in several applications, including high-speed flows with droplets, bubbles, and particles and hypervelocity impact and penetration. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with level-set interface tracking is attractive. In this regard, the ghost fluid method has been widely used to capture the interface dynamics. However, ghost fluid method experiences difficulties, particularly when strong shocks impinge on the interface. It has been shown that an accurate representation and decomposition of the wave systems (by solving a Riemann problem at the interface) significantly alleviates the shortcomings confronted by the ghost fluid method. Variants of the ghost fluid method proposed in the past differed in the way in which this Riemann problem was invoked at the interface. In this work, a simple, robust, and multidimensional procedure to construct the Riemann problem at the interface is presented. The work focuses primarily on resolving interface dynamics due to strong shocks interacting with embedded fluid-fluid interfaces (gas-gas and gas-liquid interfaces) in compressible flows. Several one- and two-dimensional problems involving moderate-to-very-large deformation of the embedded interface have been computed. The numerical examples demonstrate the flexibility, stability, and versatility of the approach in successfully resolving the embedded material interface.