A new convected level-set method for gas bubble dynamics

Abstract

The rise of bubbles in viscous liquids is not only a widespread process in many industrial applications but also an essential fundamental problem in fluid physics. The modeling and simulation of such problems is still an area of active research, mainly when surface tension is present, as in the case of single and multiple bubbles rising in viscous liquids. We treat the interface between the two fluids by a modified level-set method, called convected level-set. The difference to the standard level-set method is that the re-initialization step is embedded in the convection equation, avoiding a separate step during the calculation. In this work, we use a new truncated signed distance function to get a smooth truncation close to the interface. We couple this interface-capturing method with the Navier-Stokes equations, and we apply a global mass conservation procedure to enforce the mass balance between phases. We implement the whole model in libMesh, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement. Numerical results are presented for 2D and 3D bubble problems, and quantities of interest are compared with others. We also compare our results with experimental observations, both in the aspect of terminal bubble shapes and terminal bubble velocities, for several regimes of single and multiple bubbles rising in viscous liquids.