Efficient Numerical Simulations of Oceanic Flows with Application to Coastal Modeling

University Of South Carolina At Columbia, Columbia SC

Investigators

Abstract

Coastal ocean modeling has been developed for better serving climate impact assessments that are closely related to pressing society problems such as coastal flooding. To resolve multiple scales in ocean circulations and deal with complicated coastal topography, it is quite natural to use multi-resolution meshes in numerical simulations of oceanic flows. Typically, the grid sizes would vary from 100 km in major ocean basins to 1km in coastal regions. This, however, brings grand computational challenges: During explicit time integrations, the time step size would be restricted by the smallest grid size in the entire domain. Such a small time step size would make the numerical simulations unaffordable, especially for the purpose of climate modeling because long-term simulations are needed in such applications. To overcome this issue, this project puts forth new schemes that will be substantially more efficient compared to current algorithms used in ocean models while keeping their fidelity. This award will support one graduate student each year. We propose innovative, efficient numerical methods for simulating oceanic flows with application to coastal modeling. The new approaches comprise two major mathematical and computational developments: (i) conservative local time stepping, which allows the use of spatially-variable time step sizes in regions of different resolutions while keeping desired physical quantities conserved; and (ii) structure-preserving reduced order modeling, which significantly decreases the spatial dimension while maintaining the inherent Hamiltonian structure in the resultant low dimensional model. These approaches provide fast yet accurate and stable numerical solvers for simulating oceanic flow problems, which would enhance the simulation capability of current coastal ocean modeling and further increase computational efficiency required to solve pressing society problems such as coastal flooding. As a first step, we will study the shallow water equations on an unstructured, multi-resolution mesh. The effectiveness of the proposed methods will be demonstrated by verifying their stability and numerical accuracy. More complicated test cases and real-world applications will be further considered in this project. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.