Nodal discontinuous Galerkin spectral formulation for mooring problems with snap loads, including bending and torsion

• A high-order DGSEM method is proposed to simulate mooring lines. • The DGSEM captures wave propagation and discontinuous snap load events. • The mathematical model includes bending and torsion with high-order strain gradients. • The model has superior accuracy compared to traditional methods. • Verification shows accuracy, convergence, and suitability for complex dynamics. High-resolution numerical schemes remain underutilized in mooring line analysis of floating wind turbines and wave energy converters. The need to simulate impulsive dynamics such as snap loads — propagation of abrupt tension variations along the line — also requires shock-capturing methods capable of robustly handling these phenomena across a wide range of mooring materials, configurations, and load conditions. This work presents a nodal discontinuous Galerkin spectral element method for solving the non-linear dynamic equations of submerged mooring lines with high-order accuracy and low-dispersion errors, essential for wave propagation problems. The model accounts for hydrodynamic forces via Morison’s equation, includes current loading, seabed contact, and incorporates bending and torsional effects that preserve high-order strain gradients. Comprehensive validation and verification against analytical, numerical, and experimental benchmarks from the literature demonstrates the method’s superior accuracy and performance, and its robustness for handling slack cable conditions conducive to snap loading. This capability is particularly critical for offshore renewable energy applications where accurate prediction of these loads is essential to prevent premature failures.