  Many experiments in biomedical applications and other disciplines use a shock
tube. These experiments often involve placing an experimental sample within a
fluid-filled container, which is then placed inside the shock tube. The shock
tube produces an initial shock that propagates through gas before hitting the
container with the sample. In order to gain insight into the shock dynamics
that is hard to obtain by experimental means, computational simulations of the
shock wave passing from gas into a thin elastic solid and into a nearly
incompressible fluid are developed. It is shown that if the solid interface is
very thin, it can be neglected, simplifying the model. The model uses Euler
equations for compressible fluids coupled with a Tammann equation of state
(EOS) to model both compressible gas and almost incompressible materials. A
three-dimensional (2D axisymmetric) model of these equations is solved using
high-resolution shock-capturing methods, with newly developed Riemann solvers
and limiters. The methods are extended to work on a mapped grid to allow more
complicated interface geometry, and they are adapted to work with adaptive mesh
refinement (AMR) for higher resolution and faster computations. The Clawpack
software is used to implement the method. These methods were initially inspired
by shock tube experiments to study the injury mechanisms of traumatic brain
injury (TBI).
