A modelling approach for deformable gas bubbles

This work contributes to the field of numerical simulation of multiphase flows with a focus on gas bubbles in liquids. The immersed boundary code PRIME allows the explicit capture of phase boundaries of the solid-liquid and solid- gaseous type. The present work contributes to a third boundary type, the interface between gas and liquid as it appears in bubbly flows. This is a challenge due to the deformability of the bubbles. The basic idea is two-fold: first, the interface motion and the interfacial forces are derived from the Navier-Stokes equations, allowing a Lagrangian specification of the surface motion and the surface loads. Second, based on these equations of motion, the bubble shape is captured via a non-local parametric representation. Thus, the bubble is explicitly known as a continuous object. This is an essential difference to conventional methods, where it is common to define the surface position via marker points or, implicitly, by an indicator function. Through this continuous, Lagrangian representation, the bubble can change position and shape and is coupled locally with the fluid field.