# Integration Schemes Explicit Integration: Xn+1 – Xn = Dt . F(Xn)

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Integration Schemes Explicit Integration: Xn+1 – Xn = Dt . F(Xn)
Simple, no iteration required Time-step limited, i.e. is conditionally stable Good for short-duration phenomena (clashing & snatching) Conditional stability  ’guaranteed’ accuracy Implicit Integration: Xn+1 – Xn = Dt . F(Xn+1) Stable, large time-steps, but requires iteration Can lose accuracy,at large time steps - this needs to be assessed Can miss short-duration phenomena (contact, axial waves, etc) An implicit integration scheme for OrcaFlex is under development

Time Step Determination
Recommended Value: 1/20th of the smallest nodal natural period in the model Alternative Approaches: Increase smallest nodal period Push our luck & use larger time steps

Increasing Nodal Natural Period
Which Component Dominates? Axial Stiffness: Reduce stiffness generally, avoiding excessive stretch Reduce stiffness locally in areas requiring fine segmentation Bending Stiffness: Use longer segments, provided system allows it (check). This has a double effect as decreases the number of nodes as well as increasing time step. Consider modelling termination heads etc. with buoys

Increasing Time Step Default Value: Trial and Error Approach:
Based on experience rather than theory Errs on the conservative side Trial and Error Approach: Try twice recommended value Try three times recommended value Keep increasing until code diverges Caveat: Very occasionally produces noisy results - Check

General Run Time Considerations
Interactions between Objects: Shapes and Seabed: Avoid excessive contact stiffness Line clashing: Use clash energy as a measure of severity of impact Only enable line clashing where needed Torsion Modelling: Do you really need it? Do a check run and find out Live Graphs during Simulations: Don’t have more than you need, especially range graphs. Random Sea Cases: Outer Time Step: Recommended value may be unnecessarily small for stiff systems.

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