Quoted from: http://adcirc.org/home/documentation/users-manual-v50/introduction/ 

ADCIRC is a highly developed computer program for solving the equations of motion for a moving fluid on a rotating earth. These equations have been formulated using the traditional hydrostatic pressure and Boussinesq approximations and have been discretized in space using the finite element (FE) method and in time using the finite difference (FD) method.

ADCIRC can be run either as a two-dimensional depth integrated (2DDI) model or as a three-dimensional (3D) model. In either case, elevation is obtained from the solution of the depth-integrated continuity equation in Generalized Wave-Continuity Equation (GWCE) form. Velocity is obtained from the solution of either the 2DDI or 3D momentum equations. All nonlinear terms have been retained in these equations.

ADCIRC can be run using either a Cartesian or a spherical coordinate system.

The GWCE can be solved using either a consistent or a lumped mass matrix (via a compiler flag) and an implicit or explicit time stepping scheme (via variable time weighting coefficients). If a lumped, fully explicit formulation is specified, no matrix solver is necessary. In all other cases the GWCE is solved using the Jacobi preconditioned iterative solver from the ITPACKV 2D package.

The 2DDI momentum equations are lumped and therefore require no matrix solver. In 3D, vertical diffusion is treated implicitly and the vertical mass matrix is not lumped, thereby requiring the solution of a complex, tri-diagonal matrix problem over the vertical at every horizontal node.

ADCIRC boundary conditions include:

• specified elevation (harmonic tidal constituents or time series)
• specified normal flow (harmonic tidal constituents or time series)
• zero normal flow
• slip or no slip conditions for velocity
• external barrier overflow out of the domain
• internal barrier overflow between sections of the domain
• surface stress (wind and/or wave radiation stress)
• atmospheric pressure
• outward radiation of waves (Sommerfield condition)

ADCIRC can be forced with:

• elevation boundary conditions
• normal flow boundary conditions
• surface stress boundary conditions
• tidal potential
• earth load/self attraction tide

ADCIRC includes a least squares analysis routine that computes harmonic constituents for elevation and depth averaged velocity during the course of the run thereby avoiding the need to write out long time series for post processing.

ADCIRC has been optimized by unrolling loops for enhanced performance on multiple computer architectures. ADCIRC includes MPI library calls to allow it to operate at high efficiency (typically better than 90 per cent) on parallel computer architectures.