The simulation of compressible multi-medium flow II. applications to 2D underwater shock refraction

In this work, the methodology developed in Part I [Liu TG, Khoo BC, Yeo KS. The simulation of compressible multi-medium flow. I. A new methodology with test applications to ID gas-gas and gas-water cases. Comp. and Fluids 2000;30:291-34] is applied to study underwater shock refracting at a gas-water interface. The reflected wave is always a shock (rarefaction) wave if a shock (rarefaction) wave enters from a gas medium into water, while the reflected wave is always a rarefaction (compression) wave if the incident shock (rarefaction) wave enters from water into a gas medium. In the first study of a vertical planar underwater shock interacting with a cylindrical gas bubble, regardless of the strength of incident shock, shock refraction at the gas bubble surface is regular initially and transforms into the irregular type before the incident shock reaches the top/bottom section of the bubble. In the second study of an underwater explosion near the free surface, the dominant physical phenomena in the earlier stages of explosion consist of the outward propagation of an underwater shock. The symmetrical expansion of a gas bubble and the possible generation of a second shock inside the expanding gas bubble. At a later stage, the underwater shock refraction at the free surface begins resulting in the generation of a pair centered Prandtl-Meyer waves, and the latter interacts with the expanding gas bubble. The numerical results exhibit all the physical phenomena described by Ballhaus and Holt [Phys. Fluids 17 (1974) 1069].