An hp-adaptive discontinuous Galerkin method for modelling snap loads in mooring cables

This paper focuses on modelling snap loads in mooring cables. Snap loads are a known problem for the established oil and gas industry, and they pose a major challenge to robust mooring design for the growing industry of wave energy conversion. We present a discontinuous Galerkin formulation using a local Lax-Friedrich Riemann solver to capture snap loads in mooring cables with high accuracy. An hp−adaptive scheme is used to dynamically change the mesh size h and the polynomial order p, based on the local solution quality. We implement an error indicator and a shock identifier to capture shocks with slope-limited linear elements, while using high-order Legendre polynomials for smooth solution regions. The results show exponential error convergence of order p + 1∕2 for smooth solutions. Efficient and accurate computations of idealised shock waves in both linear and nonlinear materials were achieved using hp−adaptivity. Comparison with experimental data gives excellent results, including snap load propagation in a mooring chain. Application on a wave energy device using coupled simulations highlights the importance of the touch-down region in catenary moorings. We conclude that the formulation is able to handle snap loads with good accuracy, with implications for both maximum peak load and fatigue load estimates of mooring cables.