A moving-mesh relaxation scheme for one-dimensional barotropic two-phase flow with cavitation

Cavitation is commonly defined as a phenomenon in a liquid-flowing system when the pressure of the liquid falls sufficiently low in some region of the flow so that vapor bubbles are formed. The study of the dynamics of cavitation is an active research in many fields of science and engineering. Typical examples in relation to various features and characteristics of cavitating flows can be found, for example, at the website: http://en.wikipedia.org/wiki/Cavitation, and references therein. To compute cavitating flow numerically, one popular approach is to use a barotropic two-phase model (cf. [?]) in that, if we ignore the physical effects such as mass transfer, surface tension, and viscosity, the Eulerian formulation of the basic conservation laws in one space dimension takes the form