Method Comparison

In general, the direct method will solve a subset of problems that can be solved by the pseudo-timestepping method. This subset includes most problems of practical interest. The main restrictions or differences are outlined below.

The direct method is primarily applicable to in-bank problems and will not solve side spills. If a channel would have flooded over a side spill, a warning is given in the zzd file detailing where this would have occurred.

The direct method will cope with most of the hydraulic units available within Flood Modeller. However sluice gates cannot be solved in 'water remote' mode and the method will not yet cope with negative flows through structures.

The direct method will not accept negative flow boundaries (except at junctions), downstream flow-time boundaries or upstream head-time boundaries as these may lead to indeterminacy of the equations.

The cross-sections of a geometrically defined conduit (Circular Conduit or Rectangular Conduit for example) are not permitted to vary within a conduit reach. The open channel sections should be input from upstream to downstream, as is the normal Flood Modeller procedure.

No initial conditions, except for initial estimates of flows at confluences, are required by the direct method. Faster convergence is achieved with better initial conditions.

In general, when there is zero flow in certain reaches, these should be included in the initial conditions. It is possible that in certain reaches with zero flow the water levels cannot be calculated. Such a situation may arise between two structures with closed gates for example. In which case, the stages at nodes in the reach will be written by the direct method as -9999.0 and written as such to the Simulation Results. These must be changed before proceeding to an unsteady run.

Formally, the direct method is fourth order in accuracy and is thus more accurate than the pseudo-timestepping method, which is second order accurate at best. Inevitably there may be a small difference in the results produced by the two methods. This may cause unsteady model runs not to start smoothly and, for sensitive problems such as steep channel networks, instability may result. This can be dealt with by using the steady state results file rather than the initial conditions in the datafile for the initial conditions of the unsteady run. In this case some smoothing iterations are performed prior to the run. Alternatively results from the direct method can be used as initial conditions for a pseudo-timestepping run, the results of which would be used to initiate the unsteady run.

Another reason why the direct method may produce results that are different to the pseudo-timestepping method is the addition of automatically interpolated cross-sections, which will occur when a solution cannot be found to the required accuracy using the section spacing in the datafile. Details of how many (and at which locations) extra sections have been added by the direct method can be found in the zzd file. Experience indicates that for most problems, it is worth adding extra sections to the network using Interpolate units when the direct method has added seven or more sections. As a quick rule of thumb the following table may be useful.

Common sense needs to be used when interpreting whether another section does need to be added or whether it is the model highlighting a problem caused by another factor, such as an area of very low flow. If a very small spacing between sections is indicating that sections need to be added it is likely that cross sectional spacing is not the problem. When the interpolated sections have been added to the datafile, the model can be re-run using the direct method to check that no further interpolated sections are required.