Algebraic coupling of 2D and 3D shallow water finite element models

Baroclinicity in oceans may necessitate the use of 3D shallow water (SW) models for accurate description of physics. Particularly for baroclinic flows near coastal areas where frequent wetting and drying occurs due to tides and wind, we need a 3D SW model that can handle wetting and drying. Various methods for wetting and drying in 2D SW models are available, but for 3D SW models, wetting-drying remains a challenge. We propose using non-overlapping coupled 2D-3D models for taking advantage of well-tested 2D wetting-drying techniques and avoiding the complexities of 3D wetting and drying. We develop a theory for algebraic coupling of 2D and 3D SW models in a conforming, continuous Galerkin finite element framework, with mass and momentum conservation across the 2D-3D interface built into the coupling. This leads to a monolithic system of equations to be solved at each time step. The theory reduces to the usual finite element method when applied to 2D-2D or 3D-3D coupling. We verify 2D-3D coupling against two test cases with known analytical solutions. The results of 2D-3D coupled models for the test cases are in good agreement with the analytical solution and those of equivalent full-2D and full-3D SW models.