On Using Adaptive Mesh Refinement and Riemann Solver Based Two-Layer Shallow Water Solvers to Model Internal Tides

We present preliminary results which investigate the utility of modeling
internal tides leveraging adaptive mesh refinement and a shock-capturing finite
volume solver for the two-layer shallow water equations, both implemented in the
GeoClaw package. The adaptivity holds the promise to not only reduce
computational overhead but also for the spanning of multiple spatial and
temporal scales efficiently and only when needed temporally. The finite volume
solver for the two-layer shallow water equations allows for the accurate
representation of waves and their speeds by solving a Riemann problem for the
fully coupled system. This can reduce diffusive error and, due to the shock-
capturing nature of the approach, has the possibility to allow for more accurate
results. Additionally, GeoClaw has already been used for storm surge, tsunamis
and other pressure and wind driven flows and holds the promise of combining all
these effects in an efficient and accurate manner.