A finite volume numerical approach for coastal ocean circulation studies: Comparisons with finite difference models

TLDR

An unstructured grid, finite volume, three‑dimensional primitive‑equation coastal ocean model (FVCOM) was developed to study coastal ocean and estuarine circulation. The study compares FVCOM simulations with analytical solutions and two finite‑difference models across idealized cases of wind‑induced waves, tidal resonance, freshwater discharge, and thermal boundary layers. FVCOM employs a finite‑volume method on unstructured triangular grids, integrating mass, momentum, and heat equations to preserve conservative laws, and its results are benchmarked against the Princeton Ocean Model and ECOM‑si. FVCOM achieves improved numerical accuracy by better fitting coastline curvature, accurately capturing tide, wind, and buoyancy‑induced waves and.

Abstract

An unstructured grid, finite volume, three‐dimensional (3‐D) primitive equation coastal ocean model (FVCOM) has been developed for the study of coastal ocean and estuarine circulation by Chen et al. (2003a). The finite volume method used in this model combines the advantage of finite element methods for geometric flexibility and finite difference methods for simple discrete computation. Currents, temperature, and salinity are computed using an integral form of the equations, which provides a better representation of the conservative laws for mass, momentum, and heat. Detailed comparisons are presented here of FVCOM simulations with analytical solutions and numerical simulations made with two popular finite difference models (the Princeton Ocean Model and Estuarine and Coastal Ocean Model (ECOM‐si)) for the following idealized cases: wind‐induced long‐surface gravity waves in a circular lake, tidal resonance in rectangular and sector channels, freshwater discharge onto the continental shelf with curved and straight coastlines, and the thermal bottom boundary layer over the slope with steep bottom topography. With a better fit to the curvature of the coastline using unstructured nonoverlapping triangle grid cells, FVCOM provides improved numerical accuracy and correctly captures the physics of tide‐, wind‐, and buoyancy‐induced waves and flows in the coastal ocean. This model is suitable for applications to estuaries, continental shelves, and regional basins that feature complex coastlines and bathymetry.