This paper presents the development of an accurate and robust numerical modeling of instability of an interface separating two-phase system, such as liquid–gas and/or solid–gas systems. The instability of the interface can be refereed to the buoyancy and capillary effects in liquid–gas system. The governing unsteady Navier–Stokes along with the stress balance and kinematic conditions at the interface are solved separately in each fluid using the finite-volume approach for the liquid–gas system and the Hamilton–Jacobi equation for the solid–gas phase. The developed numerical model represents the surface and the body forces as boundary value conditions on the interface. The adapted approaches enable accurate modeling of fluid flows driven by either body or surface forces. The moving interface is tracked and captured using the level set function that initially defined for both fluids in the computational domain. To asses the developed numerical model and its versatility, a selection of different unsteady test cases including oscillation of a capillary wave, sloshing in a rectangular tank, the broken-dam problem involving different density fluids, simulation of air/water flow, and finally the moving interface between the solid and gas phases of solid rocket propellant combustion were examined. The latter case model allowed for the complete coupling between the gas-phase physics, the condensed-phase physics, and the unsteady nonuniform regression of either liquid or the propellant solid surfaces. The propagation of the unsteady nonplanar regression surface is described, using the Essentially-Non-Oscillatory (ENO) scheme with the aid of the level set strategy. The computational results demonstrate a remarkable capability of the developed numerical model to predict the dynamical characteristics of the liquid–gas and solid–gas flows, which is of great importance in many civilian and military industrial and engineering applications.
Solution of the two-phase Stefan problem by using the Picard's iterative method