RMA2 Features

RMA2 is a two dimensional depth averaged finite element hydrodynamic numerical model. It computes water surface elevations and horizontal velocity components for subcritical, free-surface flow in two dimensional flow fields. RMA2 computes a finite element solution of the Reynolds form of the Navier-Stokes equations for turbulent flows. Friction is calculated with the Manning's or Chezy equation, and eddy viscosity coefficients are used to define turbulence characteristics. Both steady and unsteady state (dynamic) problems can be analyzed.

Basic Equations

The full nonlinear shallow water equations, depth averaged to two dimensions, together with the continuity equation, are used in this model. Turbulent energy is represented by an eddy viscosity analogy. Forces due to bottom friction, wind stress and Coriolis effects are also included. The model is also capable of representing the influence of a fixed baroclinic distribution.


The approach used is the finite element method, which represents the continuum as a series of discrete elements connected at nodes and develops a solution for the reduced system. Elements consist of curved quadrilaterals, triangles and line elements. An implicit time scheme is used for time dependent systems. Several iterations are required for each solution.


  • The use of the shallow-water and hydrostatic assumptions with several options for turbulence closure.
  • All non-linear terms are included.
  • Direct solution of steady state problems and longer time steps with the implicit solution for dynamic problems.
  • A capacity to include one-dimensional and two-dimensional elements within a single mesh as appropriate.
  • Unstructured mesh form, so that extra detail can be applied in areas of special interest.
  • The ability to represent irregular boundary configurations.
  • No, partial and full slip conditions can be applied at both lateral boundaries.
  • Elements can be made wet and dry during a simulation.
  • It is supplied in FORTRAN source which has been streamlined to provide improved performance with vectorizing compilers.


The model is well suited for simulation of tidal hydrodynamics of estuaries and bays, complex riverine environments such as bridge crossings, and other systems where two dimensional flow regimes exist.