Time Step Control

Time step control features includes options for defining simulation period and time step amongst other parameters for the different modules.

Time step type

The drop-down menu includes three time step types:

·         Fixed time step

·         Tabulated time step

·         Adaptive time step

The required definition of time step depends on the selected time step type. The time step type dependent specification is described below.

Time step definition

Rainfall runoff time step multiplier

If the simulation of rainfall runoff (RR) module has been enabled together with the hydrodynamic module (HD) in the Modules page, the simulation will run the two processes in parallel (HD and RR). RR- and HD-modules will typically operate on different time-scales where RR typically require larger time steps than what is required for the HD-module. The RR time step multiplier is there­fore available to define the time step to use for the RR-module in case the two modules are simulated in parallel. RR time step will be the multiplum of the time step defined for the HD-model.

Fixed time step

Simulation uses a fixed time step throughout the entire simulation.
The fixed time step must be entered as a number and the time unit selected from the drop-down menu (seconds, minutes, hours or days).

Tabulated time step

The tabulated time step is an option for having a temporal varying time step throughout the simulation. Tabulated time step is defined using a time series from a time series file (dsf0). Click on the Browse button ‘...’ to select an exist­ing time series file or to create a new file.

Note: Time series must have the item type definition defined as ‘Time Step’ to be used as a Tabulated time step in a River simulation.

Adaptive time step

If Adaptive time step is selected, the simulation automatically maximises the time step while ensuring that all user-defined criteria are met. The mandatory criteria includes:

·         Minimum/maximum/unit: Defines the limits for the adaptation of the time step.

·         Maximum increase factor: The maximum allowable increase in time step, defined as a factor/ratio (e.g. 10% increase = 1.10)

The following criteria may be enabled and defined:

·         |resid(BC)/BC| is a measure for the largest acceptable error introduced at the boundaries. The simulation interpolates the boundary values between t and t+dt using linear interpolation. In case the boundary val­ues has a resolution finer than dt this may introduce unfavourable behav­iour where details are neglected. The term resid(BC) describes the residual between the actual value in the time series boundary condition (BC) file and the value found using linear interpolation between t and t+dt.

·         |delQ| is a measure for the largest acceptable discharge change any­where in the grid within a time step. The criteria helps to lower the time step when sudden changes appears in the discharge. The changes may be either physical changes due to a sudden increase in inflow for instance or mathematical changes due to numerical instability. In either case a decrease in time step may well be desirable.

·         |delQ/Q| is a measure for the largest acceptable relative discharge change anywhere in the grid within a time step.The criteria helps to lower the time step when sudden changes appears in the discharge. The changes may be either physical changes due to a sudden increase in inflow for instance or mathematical changes due to numerical instability. In either case a decrease in time step may well be desirable. The criteria is well suited for dam break studies where it can be used for refining the time step in the period after the break.

·         |delh| is measure for the largest acceptable water level change any­where in the grid. As for the |delQ| and |delQ/Q| criteria this criteria helps lowering the time step when large changed appears in the water level due to either physical changes or mathematical instabilities.

·         |delh/D| is measure for the largest relative acceptable water level change anywhere in the grid. As for the |delQ|, |delQ/Q| and |delh| crite­ria this criteria helps lowering the time step when large changed appears in the water level due to either physical changes or mathematical insta­bilities.

·         |Courant| (HD) specifies the maximal allowed courant number within the grid and time step. The courant number, defined above, expresses the length in terms of grid cells that information travels within a time step. The HD Courant number refers to the momentum equation and Dx is hence in this context the distance between two h-points. The simulation applies a 6-point Abbott scheme for solving the equation which does not have the typical Courant number below one demand. Good results are obtained up to Courant numbers as high as 10-20.

·         |Courant| (AD) specifies the maximal allowed courant number for the advection dispersion calculation. The AD Courant number, defined above, is a measure for the length in terms of grid cells that the species are convected within a time step. The applied computational scheme is stable for AD Courant numbers less than 1. The AD solver includes both h- and Q- points as species grid points, hence the Dx is half the distance between two h-points when calculating the AD Courant number. The cri­teria is well suited for ensuring stability of AD calculations by lowering the time step when the flow velocity increases and increasing the time step when the flow velocity decreases.