ENH : BDF-2 implementation

KikeM / romtime

Unsteady Finite Element Reduced Order Model for Time Moving Domains

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ENH : BDF-2 implementation #2

Closed KikeM closed 3 years ago

KikeM commented 3 years ago

[ ] Review BDF-2 definition in the manuscript.
[x] Implement.
Test:
- [x] Test for existing BDF-1 solution.
- [x] Test for BDF-2 solution, use conservation of mass as a validation.

See references:

integration-seance3.pdf

KikeM commented 3 years ago

I am finally implementing this because I have realised how slow it is to produce results due to the small time step I need to take (1e-3) to produce meaningful results.

Reminds me of Steven's words about better algorithms: "Computers have peaked, so we can only reach more detailed solutions with better algorithms".

KikeM commented 3 years ago

Not surprisingly, I can now cut by half the number of timesteps and yet obtain a better mass conservation.

Well done!

I am quite happy with this feature, because I consider it is the kind of functionality one might inject since the beginning but it doesn't actually change anything about the Reduced Order Model by itself. Thus, I only implemented it when the number of time steps became a problem.

Let problems show up before you fix them ;)