Supercritical Flows

Supercritical flow can be modelled approximately in Flood Modeller. This is achieved by neglecting the dA/dx part of the convective momentum term in the momentum equation when the Froude number exceeds a specified upper value. Between this upper value and a specified lower value, the term is gradually phased out so that a smooth transition is achieved.

For steady supercritical flow in a uniform channel, the method should be acceptably accurate but will become more approximate as the channel becomes more non-uniform.

This approach is adequate for problems where supercritical flow prevails locally in isolated areas of a model and when low flows are required as initial conditions for an unsteady run.

Since Flood Modeller solves the differential form of the momentum equation, the solution at a hydraulic jump or bore can never be accurate. Instead of a sharp change in stage, the change will be spread over several nodes.

Direct Method Transcritical Solver

The Direct Method steady state solver incorporates an optional accurate supercritical and transcritical flow solver which has the capability of modelling hydraulic jumps and supercritical flow more accurately. The full St Venant equations are used, with the numerical scheme reversing the direction of integration to upstream-to-downstream in supercritical parts of reaches. Momentum considerations are then used to establish where the supercritical and subcritical regimes meet, thus determining the locations of hydraulic jumps.

To use the accurate transcritical solver, one must ensure that the "Direct Method Transcritical Solver" option is selected from the Options Tab in the 1D Scenario Data window

Scope

• The Transcritical Solver is limited to the Direct Method, and cannot be used for unsteady, steady timestepping or Flood Routing models.
• Levels at upstream nodes of reaches (for example immediately downstream of junctions) may default to critical depth if no appropriate supercritical depth can be calculated by the solver.
• The flow equations at many structures contain implicit assumptions about subcritical flow and may not be appropriate for supercritical flow. Furthermore, the Direct Method Transcritical Solver calculates a downstream water level from the upstream level, which is not necessarily unique.