2   5  7   11          21        31
    - --- -- ---- ----------- --------- ---------
   |X|   |  |TIME|           |         |         |
    - --- -- ---- ----------- --------- ---------
       |  |   |           |       |         |
       |  |   |           |       |     (3) Start Time (F10.0) (default zero)
       |  |   |           |       |
       |  |   |           |       |_(2) Value of Time-step (F10.0) (default 0.1s)
       |  |   |           |
       |  |   |           |_(1)Number of Time-steps (I10) (default 10)
       |  |   |
       |  |   |_Compulsory Data Record Keyword (A4)
       |  |
       |  |_Optional User Identifier (A2)
       |
       |_Compulsory END on last data record in Data Category (A3)

(1) This number (NT) governs the length of real time simulated, meaning the simulation time is given by (NT-1) × DT (see (2)).

(2) This important parameter (DT) governs the accuracy of the integration of the equations of motion. This value must be small enough to enable an accurate representation of the highest frequency present in the motion of a structure. Failure to do so will at best give an inaccurate simulation, and at worst will cause divergence of the integration scheme and the program will abort.

Additionally, this value should not be greater than one-tenth of the period of the characteristic wave and/or external exciting forces. The Table of Time Integration Parameters due to Wave Excitation lists the preferred wave exciting force frequencies to consider for the time step setting.

If a user-defined external force is applied on the Aqwa model, the time step should not be greater than one-tenth of the force's characteristic period. For example, the rotation speed of a floating wind turbine can be measured in revolutions per minute (RPM), and the characteristic frequency (in rad/s) of the wind excitation force on the floating wind turbine system could be approximately 2 * π * RPM * number of blades / 60. Meaning the recommended time step is no more than 6/(RPM * number of blades).

If the global structural stiffnesses are high due to fenders, joints, tethers, and/or cables in your model, you should first run a dynamic Stability Analysis to calculate the natural periods of the model. The time step should not be greater than one-tenth of the natural period if the response component at that period is significant.

Having large values for tether anchor and vessel springs (TSPA/TSPV), and Tether LAteral Vessel constraint (TLAV) may cause transient impact structural responses. The natural frequencies of each tether can be estimated using the Tether Eigensolution data record (TEIG) and are listed in the .lis file, which can be used to refine the proper time step if any failure message on tether analysis is issued.

(3) This is the time (ST) at the start of the time-history simulation period, so that the time at the end of this period is given by ST + (NT - 1) × DT. It is normally left blank or set to zero except when starting the simulation from a previous analysis or when you want to alter the initial phase of frequency-dependent parameters.

To change the time-step during the analysis, multiple TIME data records may be used, up to a maximum of 10.

General Points Regarding the Time Integration Parameters

The values of all the time integration parameters are dependent on the type of analysis, but with experience you should have no difficulty in estimating their value for any particular problem.

In addition, it should be pointed out that more program automation of these values (for example, the automatic variation of time-step based on accuracy of the integration of the equations of motion) has deliberately been avoided. This is intended to make you more aware of the approximations necessary when representing discontinuities in the motion of a structure which are typically present in non-linear simulation analysis.

The following table shows typical values of time integration parameters for a large barge or tanker. This must not be considered as an accurate guide but an indication of values to be input. If your values are considerably different from these, then it is likely that an error has been made in their estimation.

Table 23.1: Time Integration Parameters due to Wave Excitation

Program	Analysis Case	(rad/s)	Notes
Aqwa-Drift	Slow Drift Analysis		and are the finishing wavelet frequency and peak frequency of a sub-directional wave spectrum, respectively. is their maximum value among the multiple sub-directional wave spectral group.
	With wave and difference frequency QTF		is the maximum value of the wavelet frequencies among the multiple sub-directional wave spectral group.
	With wave, difference and sum frequency QTFs
Aqwa-Naut	Airy wave with the LSTF option		, where is the regular wave period (seconds) defined by the PERD data record.
	Airy wave		For an Aqwa-Naut nonlinear time domain analysis, only up to the second order perturbation characteristic frequency of the hydrostatic and wave excitation wave forces is considered here.
	Second-order Stokes wave with the LSTF option
	Second-order Stokes wave
	Fifth-order Stokes wave with the LSTF option
	Fifth-order Stokes wave
	Irregular waves with the LSTF option
	Irregular waves