SELFE: A semi-implicit Eulerian–Lagrangian finite-element model for cross-scale ocean circulation

Unstructured-grid models grounded on semi-implicit, finite-volume, Eulerian-Lagrangian algorithms, such as UnTRIM and ELCIRC, have enjoyed considerable success recently in simulating 3D estuarine and coastal circulation. However, opportunities for improving the accuracy of this type of models were identified during extensive simulations of a tightly coupled estuary-plume-shelf system in the Columbia River system. Efforts to improve numerical accuracy resulted in SELFE, a new finite-element model for cross-scale ocean modeling. SELFE retains key benefits, including computational efficiency of existing semi-implicit Eulerian-Lagrangian finite-volume models, but relaxes restrictions on grids, uses higher-order shape functions for elevation, and enables superior flexibility in representing the bathymetry. Better representation of the bathymetry is enabled by a novel, "localized" vertical grid that resembles unstructured grids. At a particular horizontal location, SELFE uses either S coordinates or SZ coordinates, but the equations are consistently solved in Z space. SELFE also performs well relative to volume conservation and spurious oscillations, two problems that plague some finite-element models. This paper introduces SELFE as an open-source code available for community use and enhancement. The main focus here is on describing the formulation of the model and on showing results for a range of progressively demanding benchmark tests. While leaving details to separate publications, we also briefly illustrate the superior performance of SELFE over ELCIRC in a field application to the Columbia River estuary and plume.