In investigating the behavior of mooring line systems for container ships under combined environmental loads, selecting the right numerical methods is crucial for achieving realistic and reliable simulations. Here are some insights based on common practices in the field:

Recommendations

• Hybrid Approaches: Consider combining methods (e.g., using FEM for the mooring lines and BEM for the fluid dynamics) to leverage the strengths of each.
• Validation: Whatever method you choose, ensure to validate your numerical results against experimental data or established benchmarks to confirm the accuracy of your simulations.
• Software Tools: Look into specialized software packages for marine applications, such as MOSES or OrcaFlex, which integrate various numerical methods tailored for mooring line analysis.

In summary, while FEM, FDM, and BEM each have their strengths, a hybrid approach that combines these methods could yield the most comprehensive insights into the mooring line behavior of container ships under various environmental conditions.

There is an analytical solution that is used in predicting the stress wave response within wire ropes as used in very deep mine shafts. It was work done in the early 90's at Wits University. I was an undergrad at time and got to play with one of the validation experiments as a laboratory exercise, but like all undergrads did not pay enough attention at the time. It might be a more useful initial approach to understanding the dynamics of your loading cases before going into discrete modelling.

The two links below might be useful in finding the source material.

https://wiredspace.wits.ac.za/items/3213cc83-0394-4eec-908d-da43d6faf6ca

https://wiredspace.wits.ac.za/items/ac468b05-4457-4e4c-9f91-255cff772a37

FEM can be used for this; a simple mathematical calculation can also be done based on the type of mooring, e.g., catenary. Tools like OrcaFlex can be used in this scenario.

Best Numerical Methods for Mooring Line Behavior

1. Finite Element Method (FEM) — The Industry Standard for Structural Fidelity

Use Case: Modeling the elastic deformation and dynamic response of mooring lines (especially catenary or taut systems), including nonlinear material behavior (like polyester or chain), tension, and stretch.

Why It Works: FEM handles distributed mass and elasticity, seabed contact, line pretension, and even 3D motion coupling with ship dynamics.

Tool Example: OrcaFlex, Ansys AQWA, or commercial FEM packages with marine modules (e.g., Abaqus with user-defined elements).

Cite this:

Bai, Y., & Bai, Q. (2014). Marine Structural Design. (Chapters on mooring analysis with FEM).

2. Finite Difference Method (FDM) — Good for Hydrodynamic Time-Stepping

Use Case: Time-domain simulations of wave–structure interaction or wave drift forces, especially when solving simplified ODEs for line dynamics or vessel surge/sway under linear wave theory.

Why It Works: Very efficient for regular/semi-regular seas, or when mooring line behavior is simplified (e.g., lumped-mass models).

Tool Example: Custom-coded MATLAB or Python simulations; sometimes used in academic codes for simplified mooring line dynamics.

Cite this:

Chakrabarti, S. K. (2005). Handbook of Offshore Engineering – FDM used for wave force time-domain integration.

3. Boundary Element Method (BEM) — Excellent for Wave-Body Interaction

Use Case: Calculating diffraction and radiation forces on the vessel due to waves, which in turn affect mooring line loading. Used primarily in frequency-domain hydrodynamics.

Why It Works: Efficient for linear wave theory in deep water; gives added mass, damping, and wave excitation coefficients.

Tool Example: ANSYS AQWA, WAMIT, MOSES.

Cite this:

Newman, J. N. (1977). Marine Hydrodynamics — foundational BEM theory for wave loading.

Hybrid Methods — The Smart Approach

Most high-fidelity mooring simulations use hybrid approaches:

BEM for hydrodynamic coefficients (RAOs, wave forces),

FEM or Lumped Mass Models for mooring line dynamics,

Time-domain coupling with multi-body dynamics solvers for vessel motion (e.g., 6-DOF).

Example:

Run hydrodynamic analysis in AQWA or WAMIT → export wave force time histories → import into OrcaFlex or your own FEM solver → simulate mooring line tension + vessel motion.