Dynamic multiscale simulation of towed cable and body

Abstract

This paper presents an alternative finite element scheme to effectively simulate the dynamics of towed cable and body system, in which the large-scale rigid body motion is coupled with the small scale elastic deformation. Unlike the classic finite element method, which is based on the Lagrangian description and employs the displacement of the cable as the basic variable, the derived finite element scheme is a mixed Euler/Lagrangian description and uses the current coordinates of the cable as the basic variable. As a result, the complicated geometric nonlinear terms that takes into account the large rigid body motion, disappear in the new finite element scheme, leading to a reduction in the accumulated error arisen from each time step. The numerical results demonstrate that the derived finite element scheme is effective and robust compared with sea trial data. The towed cable and body system undergoes large-scale rigid body motion coupled with small-scale-elastic deformation. To differentiate the rigid body motion from the total displacement, complicated geometric nonlinear effect must be included into the finite element method, which in turn becomes a source of accumulated error. This phenomenon has limited the application of the finite element method in the dynamic simulation of the towed cable and body system.