Non-Tidal Reaches

The hydrodynamic flow equations dictate a natural scale for any river reach. The factors influencing the choice of Dx and Dt are the bed slope, Manning's n value, minimum discharge, channel top width and water surface curvature.

Suggested values for Dx and Dt may be found for a river reach from the following simple rules of thumb and from the paper by Samuels P.G. (1990).

Distance step

• Cross sections should generally not be more than 20B apart, where B is the top width of the channel
• Sections should generally not be more than 1/(2s) apart, where s is the mean slope of the river
• Sections should generally not be more than 0.2 D/s apart where D is the typical depth of flow (or bankfull depth for a flood model)
• In areas where the mean flow velocity exceeds 1m/s, the wetted cross section area should not change by more than about 35% between sections

Time step

• The time step should be sufficiently small to resolve the shape of the boundary conditions
• The time step may need to be small if rapid changes occur in the model such as large gate movements
• If oscillations of water level over time and in space are observed in the model results, then it may be necessary to reduce the time step to improve stability of the computations

The constraints on minimum distances between cross sections depend often on the separation of nearby structures and the undesirability of having small separations adjacent to large separations in a reach, which reduces the order of accuracy. In general it is better where possible to avoid small separations since they usually correspond to high Courant numbers for a practical choice of timestep. In general higher Courant numbers correspond to lower accuracy (for example Wilders P. et al (1987)), and this has been demonstrated for the 4-point implicit scheme (Evans EP (1977)).