A. Quarteroni, L. Formaggia
Mathematical and Numerical models for the dynamics of rowing boats: extension of the software
Resinex, a world leading firm for marine floating systems production, in order to help its engineers in design activity and to show the reliability of offered solutions to customers, commissioned MOX a software for numerical simulation of the dynamics of moored floating structures. Buoys with both standard and virtual mooring (jumper) systems, under the principal meteo-marine conditions are taken into account. Upon reducing the mathematical model to two first-order differential evolution subsystems, time advancing is carried out using the Backward Euler implicit method. The coupling between the floating body and the cable is managed by the use of Lagrange multipliers, which ensure continuity of displacement and exchanged tension at the end point of the cable. In order to cope with the extremely high stiffness of the problem, a novel mixed finite element formulation is proposed for the spatial discretization of the cable dynamics equations. This allows a robust modelling of the extensibility of the cable, in a way that is quite similar to what commonly done in mixed formulations in incompressible fluid mechanics. The stability and accuracy of the overall procedure are validated through data from real working conditions.