Enhanced RMA


The RMA suite of hydrodynamic and water quality models form a sophisticated, robust, time series tool for the simulation of the prototype conditions and design impacts. They are very flexible models that may be used for coastal, estuarine and river simulation in steady state or dynamic mode. Assemblages of one/two/three dimensional elements may be used in the same network, thus leading to considerable computer time and cost saving in complex systems. The RMA finite element models were originally developed with the support of the U.S. Army Corps of Engineers Waterways Experiment Station (WES) for simulation of 1, 2, and 3-dimensional hydrodynamics, water quality and sediment transport in rivers, bays, and estuaries. These models form the basis of the Corps of Engineers' TABS modeling system.

» Overview

RMA2

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.

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.

Method

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.
BOSS RMS for AutoCAD allows you to quickly construct cross-sections from a contour map, by simply drawing a line across the topo map.

Capabilities

The primary features of RMA2 are:

  • 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.

Applications

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.

RMA10 Overview

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.

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.

Method

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.

Capabilities

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.

Applications

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

RMA11 Overview

RMA11 is a finite element water quality model for simulation of three-dimensional estuaries, bays, lakes and rivers. It is also capable of simulating one and two dimensional approximations to systems either separately or in combined form. It is designed to accept input of velocities and depths, either from an ASCII data file or from binary results files produced by the two-dimensional hydrodynamic model, RMA2, or the three-dimensional stratified flow model, RMA10. Results in the form of velocities and depth from the hydrodynamic models are used in the solution of the advection diffusion constituent transport equations.

RMA11 Features


RMA11 is a finite element water quality model for simulation of three-dimensional estuaries, bays, lakes and rivers. It is also capable of simulating one and two dimensional approximations to systems either separately or in combined form. It is designed to accept input of velocities and depths, either from an ASCII data file or from binary results files produced by the two-dimensional hydrodynamic model, RMA2, or the three-dimensional stratified flow model, RMA10. Results in the form of velocities and depth from the hydrodynamic models are used in the solution of the advection diffusion constituent transport equations.

Governing Equations

The two/three-dimensional advection diffusion equations are simulated for conservative and decaying constituents.

Method

The equations are solved by the finite element method. The prototype system is represented by a network of triangles and quadrilaterals / cubes and prisms that may have curved sides if desired. Within each element the model uses quadratic approximations for water quality constituents. A fully implicit solution scheme is used for solution of time dependent problems.

Constituents

  • Temperature with a full atmospheric heat budget at the water surface
  • BOD/COD
  • Dissolved Oxygen
  • The nitrogen cycle (including organic nitrogen, ammonia, nitrite and nitrates)
  • The phosphorous cycle (including organic phosphorous and phosphates)
  • Alogia growth and decay
  • Cohesive suspended sediment
  • Non-cohesive suspended sediment such as sand
  • Conservative constituents

In addition the model may be configured for other simpler constituents such as tracers and E-coli.

Capabilities

The primary features of RMA11 are as follows.

  • RMA11 shares many of the same capabilities of the RMA2/RMA10 hydrodynamics models including irregular boundary configurations, variable element size, one-dimensional elements, and the wetting and drying of shallow portions of the modeled region.
  • RMA11 may be executed in steady-state or dynamic mode. The velocities supplied may be constant or interpolated from an input file (This may be RMA2 or RMA10 output).
  • Source pollutants loads may be input to the system either at discrete points, over elements, or as fixed boundary values.
  • In formulating the element equations, the element coordinate system is realigned with the local flow direction.  This permits the longitudinal and transverse diffusion terms to be separated, with the net effect being to limit excessive constituent dispersion in the direction transverse to flow.
  • For increased computational efficiency, up to fifteen constituents may be modeled at one time, each with separately defined loading, decay and initial conditions.
  • The model may be use to simulate temperature with a full heat exchange with the atmosphere, nitrogen and phosphorous nutrient cycles, BOD-DO, algae, cohesive or non-cohesive suspended sediments and other non conservative constituents.
  • A multi-layer bed model for the cohesive sediment transport constituent keeps track of thickness and consolidation of each layer.

RMAGEN Overview

The program is designed to run in conjunction with a mouse and a graphics display screen. Its purpose is the creation of an RMA2, RMA10, or RMA11 input file that is directly suitable for input to RMA1, to edit a previous RMA2, RMA10, or RMA11 input file and/or to generate an output binary file that can replace the geometry file generated by an RMA2, RMA10, or RMA11 run.

RMAGEN Features


The program is designed to run in conjunction with a mouse and a graphics display screen. Its purpose is the creation of an RMA2, RMA10, or RMA11 input file that is directly suitable for input to RMA1, to edit a previous RMA2, RMA10, or RMA11 input file and/or to generate an output binary file that can replace the geometry file generated by an RMA2, RMA10, or RMA11 run.

Capabilities

RMAGEN has the ability to use additional data input for sloping beds in one-dimensional elements. RMAGEN also permits the user to display data values as colored points as an alternative to numbers.

RMAGEN also has the ability to lock/unlock nodal elevation values. The lock/unlock options can be accessed from the node/elev menu or after ìselecting/nodesî from the dropdown menu. This feature allows the user to manually set nodal elevations and then allow the interpolation routine to pick up values for other nodes. This option is accessed node/elev box menu. RMAGEN allows the user to load a replacement map file during processing and save the lock/unlock information on the rm1 and geo files.

RMAGEN has the capability of displaying background files. These files may be in a variety of formats, either bitmap format (bmp, pcx or png) or vector format (wmf, cgm, or pic). RMAGEN adds the capability to register corners of a loaded image using known locations of points within the image. This option is accessed from the Rdraw/Background/Register drop down menu. RMAGEN also has many other capabilities.

RMAPLT Overview

The program is designed to run in conjunction with a mouse and a graphics display screen. Its purpose is the creation of velocity vector displays, contours, and time histories from the RMA series of finite element programs. RMAPLOT supports RMAGEN, RMA2, RMA4, RMA6, RMA9, RMA10, RMA11, SED2, and SED8.

RMAPLT Features

The program is designed to run in conjunction with a mouse and a graphics display screen. Its purpose is the creation of velocity vector displays, contours, and time histories from the RMA series of finite element programs. RMAPLOT supports RMAGEN, RMA2, RMA4, RMA6, RMA9, RMA10, RMA11, SED2, and SED8.

Capabilities

Velocity vectors from RMA2, RMA6 and RMA10 simulations may be displayed in two formats within this program. They are:

  • Velocity Vectors at the nodes.
  • Velocity vectors interpolated using finite element basis functions onto a rectangular grid.

Contours may be displayed for any of the results from the models plus bathymetry developed in RMAGEN. These contours may be plotted either alone or with velocity vectors superimposed on top. When this option is used velocities saved on the RMA11 results file may be displayed. Note that this display requires version 2.0 or higher of RMA11.
Time histories and cross section values may be displayed for any of the results from the models.  Time histories may be selected for selected nodes or continuity lines.  When continuity lines time histories are selected average and total properties across the section are shown.

Areal continuity checks may be displayed for results from RMA2.

Velocity vectors may be plotted from a pre-processed file containing both measured and computed values.
Area and volume mass time history plots may be generated from 2-D applications of RMA11. Areal based plots are derived from masses on the bed, volume based plots are derived from water column concentration