A Simplified Solution to the Negative Tension Problem of a Three Dimensional Towed Underwater Cable Model

Towed underwater cables are commonly used for petroleum exploration as well as several other purposes. In marine seismic exploration surveys, a number of cables containing sensors are towed behind a vessel. Accurate simulations of towed cables are important for cable positioning, prediction, control algorithm development and other purposes.
The Finite Difference Method for solving the 3D-motion equations of a towed underwater cable is generally a good algorithm for simulating large movements of towed underwater cables, but a major weakness of the model is that the cable must have positive tension. Introducing bending stiffness in the model is the classical method of overcoming the tension problem, but this complicates the matter and increases computational cost considerably.
In this article, a simplified solution to the negative tension problem is introduced. The solution involves disconnecting the tension equation from the other equations while solving the system of coupled partial differential equations. Simulation results, with validation of the solution for both positive and negative tension cases, are presented. The simulation results show high performance for the positive tension cases, and for the negative tension simulation case the original implementation fails, while the introduced solution gives valid outputs.