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: Random seed waves Wind seed number: Random seed wind Random number generator: The random number generator used for generating the time series The default option is Mersenne Twister, which is a widely used and robust pseudo-random number generator. The Legacy is a older generator, but it may not provide as good statistical properties as the Mersenne Twister. It is available for backwards compatibility and not recommended for new simulations. 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. Requested time series length: The length of the generated time series. The generated time series will have \(N_t = 2^N\) number of time steps, where \(N\) is the smallest integer such that \(N_t\) is greater than or equal to the requested time series length divided by the time increment. That is, the generated time series will have a length greater than or equal to the requested time series length, and it will be an integer multiple of the time increment. The wave and wind seed numbers are used when generating time series (see section below) before the simulation starts. 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. Figure 1. Wave spectrum 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 3.1. 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. 3.2. 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 3.3. 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. 3.4. 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. 3.5. 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. 3.6. 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. 3.6.1. 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 . . 4. External Control System These settings are used to configure an external control system, if one is defined in the model. Static Results Co-simulation with SIMO