A Numerical Method to Solve the Static Problem of a Catenary Riser

The static configuration of a catenary riser can be obtained, with a good approximation, by a perfectly flexible cable model. However, such a model cannot deal with all the boundary conditions, as for an ideal cable there is no continuity of curvature at the touchdown point, at the top and at the points where there is change in the submerged weight. At the touchdown region, for instance, the cable model overestimates the maximum curvature. For real risers, the bending stiffness effect is relevant only at small boundary layers around the points where the cable model cannot represent well the curvature continuity. This represents a big problem in the numerical integration of the differential equation of the riser, as the leading order term is very small. One approach that can be adopted is to use firstly a perfect cable model and correct later the results with analytical expressions obtained from a boundary layer method. For a two-dimensional formulation it was already shown that this approach is very good. For a three-dimensional formulation, however, such expressions are very difficult to derive and the problem must be solved numerically. This work presents a numerical method to solve the differential equation of a catenary riser, including the bending stiffness. The results obtained are compared to analytical boundary layer solutions, for a two-dimensional case, and to a full nonlinear well-known commercial computer code.