Coastal hazards are a growing problem worldwide due to not only the current and projected sea-level rise but also due to increasing populations and economic dependence on coastal areas. Today, coastal hazards related to strong storms are one of the most frequently recurring and wide spread hazards to coastal communities today. In particular storm surge, the rise of the sea surface in response to wind and pressure forcing from these storms, can have a devastating effect on the coastline. Furthermore, with the addition of climate change related effects, the ability to predict these events quickly and accurately is critical to the protection and sustainability of these coastal areas.

Computational approaches to this problem must be able to handle its multi-scale nature while remaining computationally tractable and physically relevant. This has commonly been accomplished by solving a depth-averaged sets of fluid equations and by employing non-uniform and unstructured grids. These approaches, however, have often had shortcomings due to computational expense, the need for involved model tuning, and missing physics. Additionally, to answer some of the pressing questions regarding mitigation strategies, the ability to represent the relevant scales of protective structures (on the scale of meters) to oceanic basins (hundreds of kilometers) is critical.

In this talk, I will outline some of the approaches we are developing to address several of these shortcomings and address the multi-scale issues inherent in the problem. These approaches include adaptive mesh refinement, embedded physics and cut-cell discretizations, and more accurate model equations such as the two-layer shallow water equations. Combining these new approaches promises to address some of the problems in current state-of-the-art models while continuing to decrease the computational overhead needed to calculate a forecast or climate scenario.