Numerical Methods

The motions of the bodies and elements used in Cable Solution are calculated using the Kutta-Merson method with error-checking(based on the 5th order Rung-Kutta). If the motions after each calculated step are outside of expected values, the time step is reduced until the motions fall within the accepted range.

The model uses a 7-significant digit precision on the calculated values and integrates positions to an accuracy of 0.001 meters (greater accuracies are used as required in custom-engineered solutions such as when cable added-mass is considered). The assembly (inter-body position) error is accurate to within 1E-6 meters.

The high accuracy of the integral is necessary to compensate for sudden changes in velocity such as those associated with snap-loading.

Collisions are modelled using a geometric calculation which detects the overlap between bodies. The reaction force follows inelastic collision laws. In general, only collisions between the ocean floor and the cable are considered. If necessary, collisions between the cable and a deployment guide such as a ship cable-laying sheave may be modelled.

The fluid-body interaction is modelled using the cable-element drag relationship rescribed in literature.

A polynomial approximation of the drag on a curved cylinder is used which takes into account the cross-flow effects on the cable. The ploynoliams, FN and FC, describe the normal (perpendicular to te cable element) and tangential (parallel to the cable element) components of the force.

Figure 5-1 shows the detail of the hydrodynamic, intertial, buoyant, and gravitational forces on a single element.