Two-Dimensional Locally Adaptive Non-Hydrostatic Model for Moving Bottom-Generated Waves

In some geophysical flow phenomena, such as landslide-generated tsunamis and slow earthquake-generated waves, non-hydrostatic pressure has been shown to be crucial, resulting in an effect known as the dispersive effect. One practical approach to include such an effect is by extending the Shallow Water Equations (SWE), which can be achieved by splitting the pressure terms into hydrostatic and non-hydrostatic pressure while deriving a depth-averaged form. In the end, this model requires us to solve an elliptic system of equations to make a correction to the hydrostatic SWE approximation. However, solving the elliptic problem burdens computing time significantly. Therefore, we introduce a locally adaptive non-hydrostatic model that allows us to solve the extension locally. To achieve reliable results, the corrections need to be adapted in the area where the non-hydrostatic pressure might hold a significant role. We define these areas with a simple criterion based on the hydrostatic solution. To validate our model, we apply our model to a test case that involves moving bottom-generated waves. Our result shows that we can achieve a good agreement between the local and global models, where the former approach clearly reduces the computational time.