Hi Bernd,Thank you for the help.Could you please explain me how the step size
is determined adaptively indumux? Where can I find more details?BestHai
On Tuesday, December 2, 2014 11:12 AM, Bernd Flemisch
<[email protected]> wrote:
Hi Hai,
implementing another time discretization will be a non-trivial task. For the
implicit models, the implicit Euler method is hardcoded in
dumux/implicit/common/implicitlocalresidual.hh. In the routine
evalVolumeTerms_, the time derivative is set to the first-order finite
difference and the rest (fluxes and sources) is evaluated at the current time
step.
It should not be too difficult to implement higher-order BDF methods for a
constant time-step size,
http://en.wikipedia.org/wiki/Backward_differentiation_formula
You would only need to store additional old solutions (the Model would be the
right place for this) and to adapt evalVolumeTerms_ by choosing a higher order
stencil for the time derivative.
For a variable time-step size (which is the default in Dumux, where the step
size is determined adaptively), this will become more difficult. You can write
down BDF methods for variable step sizes, but I have neither a clue nor a
reference for this.
If you think of other time stepping schemes, where you have to evaluate the
fluxes and sources at some intermediate time steps, I would not recommend
Dumux. It might be easier with general Dune-based discretization frameworks
like dune-pdelab or dune-fem.
Kind regards
Bernd
On 12/02/2014 08:27 AM, Thanh Hai Ong wrote:
Thank you Martin for the help. I did different test by using 2p model with
box and centered Finite volume and I found what you have mentioned. Can I also
use higher order time method in Dumux?
Thank you Hai
On Monday, November 24, 2014 9:54 PM, Martin
<[email protected]> wrote:
Hello Hai,
as far as I know you usually look at strong convergence rates (every strongly
convergent sequence is also weakly convergent). That means |u-u_h| -> 0 (in the
corresponding Hilbert norm) implies strong convergence. As Christoph already
mentioned, for the box method you get in general first order accuracy: second
order for pressure which implies first order for velocity and first order in
time because of backward or forward Euler method.
For the cell centered Finite Volume Scheme with Two-Point Flux Approximation
you only achieve this rates for isotropic permeability tensors. If you want to
achieve first order for general grids and permeability tensors you can use
Multi-Point-Flux approximations.
Regards,
Martin
On 11/24/2014 05:42 PM, Christoph Grüninger wrote:
Hello Hai,
what do you mean by weak and strong convergence rate?
A student of my checked the L2 error for refined grids and time steps
with the Richards equation and the FV method. We got the expected first
order convergence.
You can find the detail in his Bachelor's thesis, but it is German
"Baccour, M.H.: Verifikationsproblem mit bekannter Lösung für die
Zwei-Phasen-Darcy-Gleichung"
Additional there was a Master's thesis by Markus Wolff, it's written in
English and might help. I haven't checked myself, Bernd told me that:
"Wolff, M.: Comparison of mathematical and numerical models for twophase
flow in porous media."
Just out of curiosity: What's your affiliation?
Bye,
Christoph
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Bernd Flemisch phone: +49 711 685 69162
IWS, Universität Stuttgart fax: +49 711 685 60430
Pfaffenwaldring 61 email: [email protected]
D-70569 Stuttgart url: www.hydrosys.uni-stuttgart.de
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