Unstructured Mesh Generation and Dynamic Load Balancing for Coastal Ocean Hydrodynamic Simulation

This work examines and improves the efficiency of numerical modeling of tides, storm surge and associated flooding on unstructured meshes. Unstructured meshes composed of triangles are frequently used for numerical simulations of the coastal ocean because they can resolve the large gap in horizontal length scales necessary for accurate simulations of total water levels. However, the accuracy and the associated computational expense of the mesh are in direct conflict, which makes the mesh development process challenging.

A comprehensive approach to automatically build sophisticated planar triangulations (meshes) is developed in a toolkit called OceanMesh2D. In this software, resolution is controlled via functions of seabed data and shoreline geometry. The most challenging step of simplifying the shoreline boundary in the mesh is made automatic with a sequence of mesh improvement strategies. The main result is that seamless regional and global modeling systems can be built in minutes to hours automatically and approximately reproducibly.

The toolkit is used to investigate the design of unstructured mesh resolution and its impact on the modeling of barotropic tides along the United States coastlines. The key findings indicate that pre-existing mesh designs that use uniform resolution along the shoreline and slowly varying resolution sizes on the continental shelf inefficiently discretize the computational domain. Instead, targeting resolution in narrow geometric features and along large topographic gradients and estuarine channels, while aggressively relaxing resolution elsewhere, leads to an efficient mesh design with an order of magnitude fewer vertices than a reference solution with comparable tidal accuracy (~3% harmonic elevation amplitudes).

Lastly, coastal ocean models with overland floodplains induce computational workload imbalances because dry elements incur zero computational cost. A capability to evenly distribute computational work dynamically as floodplain regions wet and dry during the passage of a storm is developed for the ADvanced CIRCulation model. The approach is based on partitioning the decomposition of the mesh during run time so that the that the computational load is determined by the degrees of freedom in wetted areas. I demonstrate that the implementation has a low overhead cost and speed-ups of 10-45\% can be achieved for real world coastal flooding simulations