RMA10 Features

RMA10 is a multi-dimensional (combining 1-D, 2-D either depth or laterally averaged, and 3-D elements) finite element numerical model written in FORTRAN-77. It is capable of steady or dynamic simulation of three dimensional hydrodynamics, salinity, and sediment transport. It utilizes an unstructured grid and uses a Galerkin based finite element numerical scheme. The WES Coastal & Hydraulics Laboratory version is based upon the work of Dr. Ian King of Resource Management Associates.

Basic Equations

The full nonlinear Navier Stokes equation for three dimensions together with the continuity equations are used to describe the flow. The equations are modified to make the assumption of hydrostatic pressure and transformed to a constant grid to facilitate automatic solution of the free surface problem. Salinity, temperature and suspended sediment are simulated using the advection diffusion equation coupled to density through an equation of state.


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 bricks, tetrahedra and other complex shapes. An implicit time scheme is used for time dependent systems. Several iterations are required for each solution. The model automatically generates the three dimensional system from an input plan view of 1-D and 2-D elements, and can be used in partial 1-D, 2-D and 3-D configurations.


The primary features of RMA10 are:

  • The use of the shallow-water and hydrostatic assumptions.
  • Coupling of advection and diffusion of temperature, salinity and sediment to the hydrodynamics.
  • The inclusion of turbulence in Reynolds stress form.
  • Horizontal components of the non-linear terms are included.
  • A capacity to include one-dimensional, depth-averaged, laterally-averaged and three-dimensional elements within a single mesh as appropriate.
  • No, partial and full slip conditions can be applied at both lateral boundaries.
  • Partial or no slip conditions can be applied at the bed.
  • Depth-averaged elements can be made wet and dry during a simulation.
  • Vertical turbulence quantities are estimated by either a quadratic parameterization of turbulent exchange or a Mellor-Yamada Level 2 turbulence sub-model.
  • It is supplied in FORTRAN source which has been streamlined to provide improved performance with vectorizing compilers.
  • Binary output of 3D geometry, results and restart files to minimize disk usage.


RMA10 has had extensive use in computing coastal and estuarine flows (particularly San Francisco Bay (US), Galveston Bay (US), Sydney coastal waters (Aust.) and Illawarra (Aust.) Hong Kong coastal waters.