6 Integration of the equation

6.1 The overall solution algorithm

The river flow and oil dispersion equations are solved using built-in procedures in the following manner:

  1. Solve the river water phase without oil phase - steady mode.
  2. Activate STEADY=F and ONEPHS=F.
  3. Calculate and store the ice cover allocation and surface drift field for current time step.
  4. Apply spill physical processes and integrate the oil equations using the current flow fields .

6.2 Solution of the oil dispersion equations

The numerical integration of the oil conservation equations takes place according to the following sequence:

  1. The time-step is calculated;
  2. The oil properties at the new time moment are calculated;
  3. The surface slick locations are calculated;
  4. The interlayer source terms are calculated.
An overview of each of these steps will now be given.

The time step is estimated by ROSA, based on a user-set fraction of the minimum cell-crossing time. This in turn is based on the minimum cell size, and the maximum water velocity component.

The mechanical spreading theory is used to provide information of the slick plane area at any time moment. Its value is then used in iterative procedure to find the threshold marker value so that its isoline covers the fraction of plane geometry area close enough to theoretically predicted. Any cell with marker value greater or equal marker threshold is treated as full of oil.

The mass in the slick is reduced by an equal amount determined from evaporation and dissolution rate. The amount of oil reaching the shoreline will be retained or re-entrained according to the shoreline conditions. The special zero/unity marker is used to mark the near shoreline cells filled with oil deposited. They provide the information of the location and length of the shoreline segments contaminaited.

The oil concentration variables represent the depth averaged volumetric concentration of oil in the water surface or in suspended layer. The oil exchange between the layers is governed by source terms in conservation equations. In fact, when a portion of surface oil is mixed into suspension, that amount of oil leave the former to settled into the latter. The same is true for reverse direction as well.

Sources expressing these interchanges are computed once the oil equations have been integrated. They are stored, and will be used the next time PHOENICS solves the oil phase equations.