HEC-RAS uses an iterative procedure for solving the multiple opening problem. The following approach is used when performing a multiple opening computation:

  1. The program makes a first guess at the upstream water surface by setting it equal to the computed energy on the downstream side of the river crossing.
  2. The assumed water surface is projected onto the upstream side of the bridge. A flow distribution is computed based on the percent of flow area in each opening.
  3. Once a flow distribution is estimated, the stagnation points are calculated based on the upstream cross section. The assumed water surface is put into the upstream section. The hydraulic properties are calculated based on the assumed water surface and flow distribution. Stagnation points are located by apportioning the conveyance in the upstream cross section, so that the percentage of conveyance for each section is equal to the percentage of flow allocated to each opening.
  4. The stagnation points in the downstream cross section (section just downstream of the river crossing) are located in the same manner.
  5. Once a flow distribution is assumed, and the upstream and downstream stagnation points are set, the program calculates the water surface profiles through each opening, using the assumed flow.
  6. After the program has computed the upstream energy for each opening, a comparison is made between the energies to see if a balance has been achieved (i.e., the difference between the highest and lowest computed energy is less than a predefined tolerance). If the energies are not within the tolerance, the program computes an average energy by using a flow weighting for each opening.
  7. The average energy computed in step 6 is used to estimate the new flow distribution. This estimate of the flow distribution is based on adjusting the flow in each opening proportional to the percentage that the computed energy for that opening is from the weighted average energy. An opening with a computed energy higher than the weighted mean will have its flow reduced, while an opening with a computed energy that is lower than the weighted mean will have its flow increased. Once the flow for all the openings is adjusted, a continuity check is made to ensure that the sum of the flows in all the openings is equal to the total flow. If this is not true, the flow in each opening is adjusted to ensure that the sum of flows is equal to the total flow.
  8. Steps 3 through 7 continue until either a balance in energy is reached or the program gets to the fifth iteration. If the program gets to the fifth iteration, then the program switches to a different iterating method. In the second iteration method, the program formulates a flow versus upstream energy curve for each opening. The rating curve is based on the first four iterations. The rating curves are combined to get a total flow verses energy curve for the entire crossing. A new upstream energy guess is based on entering this curve with the total flow and interpolating an energy. Once a new energy is estimated, the program goes back to the individual opening curves with this energy and interpolates a flow for each opening. With this new flow distribution the program computes the water surface and energy profiles for each opening. If all the energies are within the tolerance, the calculation procedure is finished. If it is not within the tolerance the rating curves are updated with the new computed points, and the process continues. This iteration procedure continues until either a solution within the tolerance is achieved, or the program reaches the maximum number of iterations. The tolerance for balancing the energies between openings is 5 times the normal cross section water surface tolerance (0.05 feet or 0.015 meters). The default number of iterations for the multiple opening solutions scheme is 1.5 times the normal cross section maximum (the default is 30).
  9. Once a solution is achieved, the program places the mean computed energy into the upstream cross section and computes a corresponding water surface for the entire cross section. In general, this water surface will differ from the water surfaces computed from the individual openings. This mean energy and water surface are reported as the final solution at the upstream section. User=s can obtain the results of the computed energies and water surfaces for each opening through the cross section specific output table, as well as the multiple opening profile type of table.