Understanding dynamic, implicit method: what is numerical dissipation?

[apal21]

Hello,

I am using dynamic, implicit integration (quasi-static mode) in an analysis, and I am trying to understand how it works. The documentation (

https://abaqus-docs.mit.edu/2017/English/SIMACAEANLRefMap/simaanl-c-dynamic.htm)

talks about using 'numerical dissipation'. What does that mean? How does it control how much dissipation/damping there is?

 

[FEA way]

This is basically numerical damping required to obtain convergence. In the case of quasi-static application this damping is very significant to get quasi-static solutions.

 

[apal21]

And are there any adverse effects to this numerical damping? Could it lead to instabilities which give me an un-physical answer?

 

[FEA way]

If you choose proper application type for your analysis then this numerical damping shouldn’t cause any problems. But for transient fidelity and moderate dissipation application types you can use the ALPHA parameter to define non-default value of numerical damping and see how it influences the results.

 

[apal21]

Understood. So for a quasi-static application, instability should generally not be an issue. Is that correct?

 

[FEA way]

Yes, the significant amount of damping in quasi-static application type provides stability and improves convergence when seeking for essentially static solution of a given problem.

 

[apal21]

Great, thank you!

 

[IceBreakerSours]

While I agree with the physical intuition/interpretation, it is important to remember numerical dissipation has - as the term suggests - a numerical (not physical) origin. The numerical implicit integrator solving the governing equations ends up "losing" energy as solution progresses.

Imagine running a simulation of a simple pendulum. If there is no damping, you should expect the pendulum to swing forever after an initial impulse - if there is no dissipation due to material damping, aerodynamic drag, mechanical friction, etc. As it turns out, if you ran that simulation, you will see the pendulum "slow down" over time.

Now, whether this numerical loss is meaningful or not depends entirely on the problem. If you are performing transient analysis of rotating machinery, then you may care a lot about this dissipation. On the other hand, if you are running a quasi-static model, then the numerical loss might end up benefiting you because some high frequency components to the solution might be removed making the solution manifold much smoother which allows the auto-time stepper to take longer time steps.

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