Developing Efficient High-Order Transport Schemes for Cross-Scale Coupled Estuary-Ocean Modeling

Geophysical fluid dynamics (GFD) models have progressed greatly in simulating the world’s oceans and estuaries in the past three decades, thanks to the development of novel numerical algorithms and the advent of massively parallel high-performance computing platforms. Study of inter-related processes on multi-scales (e.g., between large-scale (remote) processes and small-scale (local) processes) has always been an important theme for GFD modeling. For this purpose, models based on unstructured-grid (UG) have shown great potential because of their superior abilities in enabling multi-resolution and in fitting geometry and boundary. Despite UG models’ successful applications on coastal systems, significant obstacles still exist that have so far prevented UG models from realizing their full cross-scale capability. The pressing issues include the computation overhead resulting from large contrasts in the spatial resolutions, and the relative lack of skill for UG model in the eddying regime. Specifically for our own implicit UG model (SCHISM), the transport solver often emerges as a major bottleneck for both accuracy and efficiency. The overall goal of this dissertation is two-fold. The first goal is to address the challenges in tracer transport by developing efficient high-order schemes for the transport processes and test them in the framework of a community supported modeling system (SCHISM: Semi-implicit Cross-scale Hydroscience Integrated System Model) for cross-scale processes. The second goal is to utilize the new schemes developed in this dissertation and elsewhere to build a bona fide cross-scale Chesapeake Bay model and use it to address some key knowledge gaps in the physical processes in this system and to better assist decision makers of coastal resource management. The work on numerical scheme development has resulted in two new high-order transport solvers. The first solver tackles the vertical transport that often imposes the most stringent constraint on model efficiency (Chapter 2). With an implicit method and two flux limiters in both space and time, the new TVD2 solver leads to a speed-up of 1.6-6.0 in various cross-scale applications as compared to traditional explicit methods, while achieving 2nd-order accuracy in both space and time. Together with a flexible vertical gridding system, the flow over steep slopes can be faithfully simulated efficiently and accurately without altering the underlying bathymetry. The second scheme aims at improving the model skill in the eddying ocean (Chapter 4). UG coastal models tend to under-resolve features like meso-scale eddies and meanders, and this issue is partially attributed to the numerical diffusion in the transport schemes that are originally developed for estuarine applications. to address this issue, a 3rd-order transport scheme based on WENO formulation is developed, and is demonstrated to improve the meso-scale features. The new solvers are then tested in the Chesapeake Bay and adjacent Atlantic Ocean on small, medium and large domains respectively, corresponding to the three main chapters of this dissertation (Chapter 2-4), with an ultimate goal of achieving a seamless cross-scale model from the Gulf Stream to the shallow regions in the Bay tributaries and sub-tributaries. We highlight the dominant role played by the bathymetry in nearshore systems and the detrimental effects of bathymetric smoothing commonly used in many coastal models (Chapter 3). With the new methods developed in this dissertation and elsewhere, the model has enabled the analyses on some important processes that are hard to quantify with traditional techniques, e.g., the effect of channel-shoal contrast on lateral circulation and salinity distribution, hypoxia volume, the influence of realistic bathymetry on the freshwater plume etc. Potential topics for future research are also discussed at the end. In addition, the new solvers have also been successfully exported to many other oceanic and nearshore systems around the world via user groups of our community modeling system (cf. ‘Publications’ under ‘schism.wiki’)