Application of the generalized- α method to the time integration of the cable dynamics equations

Abstract

The box method is a popular finite difference scheme for solving the cable dynamics equations in ocean engineering applications. In this paper, we analyze the shortcomings of the temporal integration defined by the box method and propose a new procedure that retains the box method's spatial discretization, but employs the generalized- α method for temporal discretization. The stability and accuracy of the generalized- α method, as applied to the cable dynamics equations, are developed. This analysis procedure demonstrates the formulation of the semi-discrete governing equations using spatial finite differences and the applicability of amplification matrix stability analysis to finite difference problems. An example is presented that demonstrates the robustness of the new approach.