For transient groundwater modelling a temporal discretization (the increment between time points to be calculated) has to be chosen. The size of a suitable time step size depends to a great extent on the time course of the event to be described. Thus, the modelling of a flood wave requires time steps in the order of hours to a day, while for the calculation of annual series of the groundwater level fluctuation time steps of a few days to a month are allowed.

The mapping of short-term changes of withdrawal in a well may require time steps of minutes, while in a subsequent phase with unchanged production rates, the progressive enlargement of time steps is allowed.

To avoid any impact on the model results due to large time steps a sensitivity analysis can be carried out at the beginning of a project, where relatively large time steps are reduced to small time steps until no difference is seen between the results of the last two model computations. A further reduction of the time step would increase the computational effort without producing an improvement in the model results.

For the time discretization of the unsteady flow equation an implicit Euler method is used in SPRING:

with θ = 1.

 

The transient boundary conditions are by default treated fully implicit (θ = 1.0), i.e., to calculate the state at the time t_n+1, the boundary conditions of the time t_n+1 are used.

In flow rate boundary conditions is only an explicit treatment of the unsteady boundary conditions possible, i.e., to calculate the state at the time t_n+1 are the boundary conditions of the time t_n are used.

 

Special case: transport calculation