Strongly Coupled 2D and 3D Shallow Water Models: Theory and Verification

We introduce a monolithic/strong, interfacial coupling formulation between two-dimensional (2D) and three-dimensional (3D) shallow water (SW) and transport models. This coupling becomes necessary in regions such as estuaries leading into inundation areas or wetlands where wetting and drying has an effect on baroclinic regions. We present the formulation and verification of a novel method for monolithically coupling 2D and 3D SW and transport equations in an implicit-in-time, streamline upwind Petrov Galerkin (SUPG)-stabilized continuous Galerkin finite-element method (CG-FEM) setting, with a key requirement of mass and momentum conservation across the 2D–3D interface. Solutions of the method are verified against full-2D and full-3D/3D-only models. It is concluded that the formulation is conservative, stable, accurate, convergent, computationally cheaper than full-3D models when noncritical 3D regions are replaced with 2D subdomains, and capable of simulating physics that solely 2D or 3D production models are generally incapable of.