ADCIRC is both a 2-dimensional (2D) and 3D model, and the numerical formulations of these are somewhat different. The best documentation of the base model numerics for both is currently in the ADCIRC Theory Report. ADCIRC is finite element in space and finite difference in time. Solution can be carried out either semi-implicitly or in lumped explicit mode, with the latter being faster but somewhat less accurate and less stable. If not operating in lumped explicit mode, time weights at t-1, t, and t+1 can be specified in the user in the fort.15 file, and a Jacobi solver is used to solve the mass matrix.
2D ADCIRC Numerics
2D ADCIRC is based on a form of the shallow water equations, which includes the continuity equation and the horizontal momentum equations. The formulation of the continuity equation relies on the Generalized Wave Continuity Equation, or GWCE, which helps deal with the spurious oscillations that arise from the primitive Galerkin finite element formulation.