The development of efficient algorithms to understand implosion dynamics presents
a number of challenges. The foremost challenge is to efficiently represent the coupled
compressible fluid dynamics of internal air and surrounding water.

Secondly, the method must allow one to accurately detect or follow the interface between the
phases.

Finally, it must be capable of resolving any shock waves which may be created
in air or water during the final stage of the collapse.

We present a fully Lagrangian
compressible numerical framework for the simulation of underwater implosion. Both
air and water are considered compressible and the equations for the Lagrangian shock
hydrodynamics are stabilized via a variationally consistent multiscale method.

A nodally perfect matched definition of the interface is used and then the kinetic
variables, pressure and density, are duplicated at the interface level. An adaptive
mesh generation procedure, which respects the interface connectivities, is applied to
provide enough refinement at the interface level. This framework is then used to simulate
the underwater implosion of a large cylindrical bubble, with a size in the order of
cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm),
and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in
addition to the shock waves traveling in the fluid domains are among the phenomena
that are observed in the simulation. We then extend our framework to model the
underwater implosion of a cylindrical aluminum container considering a monolithic
fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal
atmospheric-pressure air from the external high-pressure water, is modeled by a three
node rotation-free shell element. The cylinder undergoes fast transient deformations,
large enough to produce self-contact along it.

A novel elastic frictionless contact model
is used to detect contact and compute the non-penetrating forces in the discretized
domain between the mid-planes of the shell. Two schemes are tested, implicit using
the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler
scheme. The results of the two simulations are compared with experimental data.