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Tradeoffs between coupling methods

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I noticed the recent addition of TLM by User:Petkr which makes me wonder if we should perhaps add something to this article on some of the tradeoffs between different coupling methods. For example TLM's usefulness is limited to timesteps on the order of the propagation time in the transmission line. This is quite short in for example a driveshaft (100s of µs), compared to the simulation of an entire vehicle (10s of ms). Similarly Jacobi is only stable for timesteps on the order of the fastest mode in the system, which is problematic for stiff systems. KetchupSalt (talk) 19:28, 6 March 2022 (UTC)[reply]

The real propagation time and timestep do not need to be the same. For the shaft example: If the TLM element is adjusted to have the right flexibility, a timestep longer than the propagation error will give a (parasitic) inertia. This can be viewed as a modelling error, but if the inertia is low enough it does not affect the simulation (e.g. there might be a much larger inertia attached to the shaft), and a modelling error is much more benign than a numerical error (i.e. conservation laws still applies).. Petkr (talk) 10:10, 13 April 2022 (UTC)[reply]
This very much depends on what you are simulating. A large inertia attached to the TLM element will attenuate the error, sure. Can this always be made the case? Excessive time delays can also cause problems, especially for stiff systems. KetchupSalt (talk) 18:25, 13 April 2022 (UTC)[reply]