The equations for conservation of mass, momentum, and energy are solved on a fixed Cartesian grid using a fully conservative higher order MUSCL scheme. The dilatational response of each material is handled using a suitable equation of state. The embedded interfaces are handled using a mixed-cell approach. This approach uses an Eulerian treatment for the computational cells away from the interface and a Lagrangian treatment for the cells including interface elements, resulting in a fully conservative method for multi-material interactions. The method has shown capability to resolve and capture non-linear waves such as shock waves, rarefaction waves, and contact discontinuities in complex geometries. This work mainly emphasizes the handling of shock-wave interaction with bubbles, bubbly media, and multi-fluid interfaces in a compressible flow framework. Several numerical examples are shown to demonstrate the validity and robustness of the method.
Kapahi, A., Hsiao, C. T., & Chahine, G. L. (2015). A multi-material flow solver for high speed compressible flows. Computers and Fluids, 115, 25–45. https://doi.org/10.1016/j.compfluid.2015.03.016