1. Numerical Procedure

1.1. Integration methods

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.

1.2. Wind Forces

Wind method options are: Options:

  • No waves: No waves are generated, and wave forces are not included in the simulation.

  • FFT only: 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), see FFT.

  • State space model: State-space model driven by white noise, see State-space model driven by white noise.

Wind time series method options are

  • Same: The same wind time series is applied to all bodies in the model.

  • Separate: A separate wind time series is generated for each body in the model. This option can be used to model spatial variation in the wind field, such as a gust that only affects one part of the model.

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

Checkbox-Option to specify the vertical domain for wind

  • Number of levels: The number of vertical levels to pre.-generate wind time series for

  • Z minimum: Lower limit vertical domain

  • Z maximum: Upper limit of vertical domain

  • Allow outside the domain: If selected, wind time series will be generated outside the specified vertical domain

1.3. 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.

1.4. Wave Generation Method

Options:

  • No waves: No waves are generated, and wave forces are not included in the simulation.

  • FFT only: The time series of wave responses are generated by superposition of harmonic components with uniformly distributed phases by means of pre-generation by the Fast Fourier transform (FFT), see see FFT.

  • Cosine: Time domain summation of the harmonic components (Cosine), see Summation of harmonic components.

  • Combined : For a more fine grained control, a combination of pregenerated time series and cosine series in the time domain is made possible.

  • Visualization: Time domain summation of the harmonic components (Cosine). This option is only available for visualization purposes.

1.5. Hydro Filter Method / Hydro System Period

The hydro filter is used for low-pass filtering or blocking (set to zero) the translational and angular velocities appearing in the Coriolis-Centripetal forces resulting from added mass. The effect of the different options will depend on body type, as explained in Equations of motion (Theory).

The default and recommended option in most cases is Block low pass translation velocities, although changing the Hydro Filter Method usually has a minor effect on the simulation results.

If the Hydro Filter Method is set to Filter activated, low-pass filtered translational and angular velocities are used in the Coriolis-Centripetal forces resulting from added mass. A 2nd order Butterworth filter with a cut-off period corresponding to Hydro System Period is used, unless any given body has defined a Method for estimating low-frequency motion. In that case, the low-frequency estimation method (low-pass filter) defined on the body takes precedence over the Hydro System Period and associated Butterworth filter.

1.6. Wave time series from file

If long-crested waves are specified, it is possible to read wave elevation time series from an ASCII file:

  • Wave scale factor: The wave elevation will be scaled by the scaling factor while the time step is scaled by the square root of the scaling factor.

  • Ref point X and Ref point Y: coordinates of the point where the wave elevation is specified

  • Water depth: Full scale water depth

  • File name: Path to the file containing the wave elevation time series

  • Filter input time series: If selected, the wave elevation time series will be filtered using a band-pass filter with specified lower and upper cut-off periods.

1.6.1. File format for wave elevation time series

File format for wave elevation time series:

  • Line 1 : Number of samples, N

  • Line 2 : Time step

  • Line 3 : Arbitrary text

  • Line 4 : Arbitrary text

  • Lines 5 to 4+N : Time series read in free format (arbitrary number of samples on each line)

Example: Wave elevation time series file with 2048 samples and a time step of 0.5 seconds
2048 ' Number of samples
.50 ' Time step
Text 1
Text 2
20.0000
20.3923
20.7822 21.1672
21.5451 21.9134
.
.