# General data: Explicit integration

## Inner time step, outer time step

For efficiency of computation, OrcaFlex uses two integration time steps when explicit integration is used in the dynamic simulation: an inner time step and a larger outer time step. Most values during the simulation are calculated at every inner time step, but some slowly-varying parameters (such as wave particle motion and most hydrodynamic and aerodynamic forces) are only recalculated at each outer time step. This reduces the number of calculations needed and so increases the speed of simulation.

The usual effect of setting one of the time steps too large is that the simulation becomes unstable, in the sense that very large and rapidly-increasing oscillations develop, usually very near the start of the simulation. OrcaFlex detects and reports most such instabilities; the time steps can then be reduced and the simulation retried. However, even in the absence of such warnings, it is generally worth repeating important simulations with smaller step sizes to confirm their accuracy.

### Recommendations for setting time steps

Both time steps must be short enough to give stable and accurate simulation. Experience indicates that the inner step should not exceed 1/10th to 1/20th of the shortest natural nodal period of motion for any degree of freedom in the model. The shortest natural nodal period is reported in the summary results for statics.

The outer step can usually be set to 10 times the inner time step; this gives a good saving in computing time without risking instability. In addition, the outer time step should generally not be more than 1/40th of the wave period (or 1/40th of the zero crossing period for a wave spectrum). If you are using a wake oscillator VIV model then we recommend that the outer time step is no more than 1/200th of the minimum wake oscillator Strouhal period.

 Note: High values of seabed stiffness may shorten the natural period of objects in contact with the seabed, which in turn will lead to shorter inner time steps being required. Beware that this effect of seabed stiffness will not be accounted for in the shortest natural period calculation if touchdown does not occur in statics.

## Always use recommended time steps

OrcaFlex helps you set the simulation time steps using the above criteria. There are 2 modes of operation:

If always use recommended time steps is checked (the default setting) then OrcaFlex will calculate recommended time steps and use these values directly. This means that any values that you specify will be overwritten.

The main advantage of using this option comes during the design phase. If you make changes to the model's properties which alter the shortest natural nodal period then OrcaFlex automatically modifies the time steps accordingly. This is particularly useful when you make a change that allows the use of longer time steps. When not using this option it is all too easy to forget to lengthen the time steps and suffer unnecessarily long simulation run times.

The other significant benefit of this mode of operation comes when preparing a large number of similar simulations using batch script methods. Suppose that the different models involved have differing shortest natural nodal periods: this option allows you to use appropriate time steps for each individual model without having to set them manually.

If always use recommended time steps is not checked then OrcaFlex still calculates the recommended time steps and, if these are shorter than the values specified on the general data form, OrcaFlex issues a warning and gives you the option of using the recommended values. You are free to disregard these warnings, but if either time step (and particularly the inner) is set too large there is a danger of instability or inaccuracy in the simulation.

This mode of operation is generally to be preferred on occasions when OrcaFlex recommends time steps which are too long, leading to an unstable simulation. Sometimes the only solution is to set the time steps manually, and this option gives you that flexibility.

## Recommended time step settings

The recommendations which OrcaFlex makes for time steps are those which we have found to work well in practice. You may, however, wish to change these recommendations, and these settings allow you to do this.

### Inner time step (fraction of shortest natural period)

Our experience is that for most cases the inner time step can safely be set to 1/10th of the shortest natural nodal period. However, for some models you may find you need to use a shorter time step to achieve a stable simulation. By changing this value you can control what fraction of the shortest natural period OrcaFlex uses to calculate the recommended inner time step. The default value is 10, which equates to a recommended inner time step of 1/10th of the shortest natural period. A value of 20 would give a recommended inner time step of 1/20th of the shortest natural period, and so on.

### Outer time step (multiple of inner time step)

The recommended outer time step will be no greater than this value times the inner time step.

### Outer time step (fraction of wave period or Tz)

The recommended outer time step will be no greater than $T$ divided by this value, where $T$ is either the wave period (for regular waves) or $\Tz$ (for random waves).

### Outer time step (fraction of wake oscillator Strouhal period)

This data item is only available if you are using a wake oscillator VIV model. The recommended outer time step will be no greater than the minimum wake oscillator Strouhal period divided by this value.