On 3/13/20 2:49 PM, Krishnakumar Gopalakrishnan wrote:
* /Yes, it's a good step. But it implies that you get a restriction on the
time step size. /
Does that become severe even if I use the present time-step for all other
terms? In the \nabla ( D(u) u) term, I will replace only D(u) with the
previous time-steps and retain the u^{n} to be at the current time-step.
So, the time-step restriction should not be as bad as the fully explicit case,
right?
Maybe, maybe not. It depends on how strong the nonlinearity D(u) is.
Obviously, if D(u) is actually constant, then there is no restriction at all.
So it's a question of how much it deviates from being a constant.
* /You can also replace D(u^n) by D(u^*) where u^* is extrapolated from the
previous two or three time steps. That's a more accurate approximation
than just using u^{n-1}. /
That sounds perfect. Thank you. Is there any suitable functions from deal.ii
that I can use for this extrapolation? Is there any tutorial that already
does something this?
Not sure. I think that step-32 does something along these lines, but I don't
recall exactly.
Best
W.
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