Numerical simulation of violent bubble motion

A robust mixed-Eulerian-Lagrangian modeling is presented for the simulation of violent bubble motion, which is characterized by implementing a hybrid surface interpolation for calculating the material velocity. A linear averaging approximation is deployed for the parts of the surface where the change of the surface normal within the element size is not small, and a polynomial scheme coupled with the weighted moving least squares method for the rest of the surface. Solid angles on the free surface (an open surface) are computed analytically in a closed form using the spherical triangle theory. The algorithm is validated against an experiment and an axisymmetric bubble code. Numerical analyses are carried out for the evolution of a gas bubble near an inclined rigid wall and the interaction of two gas bubbles and a free surface. The robustness of the algorithm is demonstrated through simulating sharp bubble jets, a bubble collapsing nearby a rigid wall with a large part of the bubble surface flattened against the wall, and bubbles collapsing in very close to a free surface producing sharp free surface spikes.