Dynamic Calculation Parameters

This editor contains all parameters available to configure the dynamic calculation of a SIMO task.

1. Main Simulation Parameters

The following parameters are available:

  • Simulation length

  • Simulation time step

The simulation time step should be chosen such that important dynamic effects are captured in the simulation. Simulations considering contact problems generally require a short time step.

2. Pregenerated Time Series Parameters

The following parameters are available:

  • Wave seed number

  • Wind seed number

  • Time increment: The time increment is the time step for the generation of load and motion time series, which is the same as the time step for the retardation functions. As such, the time increment should be chosen such that important frequencies are captured.

  • N: the number of time steps is \(N_t = 2^N\).

The wave and wind seed numbers are used when generating time series (see section below) before the simulation starts.

Note that the storage step in a simulation will be the same as the time increment.

Time series of waves, wind, first order wave loads or motions, wave drift forces etc. are required during the dynamic simulation. These time series must be generated such that they are at least as long as the full dynamic simulation and correctly represent the desired frequencies. That is, the time series length should be greater than or equal to the simulation length (to avoid repetition), and the time increment for time series generation should be appropriate for the given process. The time increment for time series generation should also be an integer multiple of the simulation time step.

As shown below, the time series (wave/wind/load/motion) are generated by discretizing the variance spectrum into a finite number of harmonic components with uniformly distributed phases using FFT. The phase angles are generated using a pseudo-random number generator with the seed given as user input. Choosing a different seed will give a different time series realization which in turn will yield different simulation results when wave and/or wind loads are included in the simulation.

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The time increment, frequency increment and maximum duration (without repetition) are interrelated when the addition of the harmonic components is performed by FFT:

\[\Delta \omega = \frac{2\pi}{N_t \Delta t} = \frac{2\pi}{T_{rep}}\]

where \(\Delta \omega\) is the frequency increment, \(N_t\) is the number of time steps (This is given implicitly by the 2^N parameter), \(\Delta t\) is the time increment, and \(T_{rep}\) is the length of the generated time series.

3. Numerical Procedure

Two integration methods are available:

  • Runge-Kutta: 3rd order Runge-Kutta-like method. A three-stage Runge-Kutta integration is used within each subdivision of the time increment.

  • Euler: Modified Euler method:

\[\dot{x}_{k+1} = \dot{x}_k + (\Delta t)f_k\]
\[{x}_{k+1} = {x}_k + (\Delta t)\dot{x}_{k+1}\]

This implementation ensures stability when the method is applied to linear models with no damping.

3.1. Wind Forces

Wind velocities will be calculated for the wind propagation direction, but a transverse gust speed may also be specified if the Wind Velocity Dimension option is set to Two dimensional. The option Wind Time Series Method specifies if the same wind time series should be used on all bodies or if a separate time series should be generated for each body.

Three methods for calculating wind forces are available:

  • Calculation of static force due to average wind velocity

  • Forces due to relative wind velocity

  • Forces due to absolute wind velocity

3.2. Current Forces

Two force models are available:

  • Calculation of static forces

  • Forces due to relative current velocity

The method can be selected for both linear and quadratic current force coefficients.

3.3. Wave Generation Method

The time series of wave responses are generated by superposition of harmonic components with uniformly distributed phases by means of pregeneration by the Fast Fourier transform (FFT) or by time domain summation of the harmonic components (Cosine). For more fine grained control, a combination of pregenerated time series and cosine series in the time domain is made possible with the combined option.

4. External Control System

These settings are used to configure an external control system, if one is defined in the model.