Hi Helena,
I just discussed this briefly with Martin. He is of course right. Nevertheless, as you are looking for a single effective quantity for your cell, one might be able to simplify things. Can you please state the cell problem exactly in terms of PDE and boundary conditions as well as the upscaling on the continuous level that you would like to perform? We might come up with a simpler solution then. Kind regards Bernd -- _________________________________________________________________ Bernd Flemisch IWS, Universität Stuttgart phone: +49 711 685 69162 Pfaffenwaldring 61 email: [email protected] D-70569 Stuttgart url: www.iws.uni-stuttgart.de/en/lh2/<http://www.iws.uni-stuttgart.de/en/lh2/> _________________________________________________________________ ________________________________ Von: DuMux <[email protected]> im Auftrag von Helena Kschidock <[email protected]> Gesendet: Freitag, 10. Februar 2023 09:05:05 An: Schneider, Martin Cc: DuMux User Mailing List Betreff: Re: [DuMux] Gradients of solution vector with TPFA Thank you Martin, I will have a look at these solutions! Best regards, Helena Martin Schneider <[email protected]<mailto:[email protected]>> schrieb am Fr., 10. Feb. 2023, 08:13: Dear Helena, if I understand you correctly, you want to calculate spatial gradients of your primary variables? This is not straight-forward for CCTPFA, at least if you have heterogeneous data. If you need the pressure gradient, you could recalculate it from the darcy velocity and simply use the existing velocity calculation in dumux (https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/dumux/porousmediumflow/velocity.hh). There is also a more generic way to calculate gradients by using for example equation (39) in https://ogst.ifpenergiesnouvelles.fr/articles/ogst/pdf/2018/01/ogst180050.pdf There, K denotes the control volume (element) for which you want to calculate the gradient of some primary variable u and u_\sigma is some approximation of your solution on face \sigma (in Dumux denoted as scvf). For CCTPFA u_\sigma can be calculated as the harmonic average of neighboring solution values with corresponding transmissibilities. If you have homogeneous data this would be simply some distance average. We are currently working on a generic way to interpolate variables and to calculate gradients, however, this is not yet available. I hope this helps. Best regards, Martin On 09.02.23 20:06, Helena Kschidock wrote: > Hi all, > > I am currently implementing a cell problem in DuMuX and am using an > adapted 1p model/Darcy Problem with CCTPFA discretization to do so. > After obtaining the solution vector, I need to obtain the gradients of > the solution which I will then use to calculate my upscaled > conductivities through integration. > > In the exchange with Dimitry Pavlov in the mailing list archive (see > 2020q2 "How to implement MaterialLawParams that depend on pressure > gradient"), Timo suggested using the Jacobian to obtain the gradients > (which I could easily make available in my case, as the step is done > AFTER solving the cell problem). However I am slightly confused - > isn't the Jacobian the partial derivative of the residual with respect > to the solution (instead of the partial residual of the solution with > respect to the dimension)? At least this is what the handbook seems to > imply. > > Thanks for any help, > Helena > > _______________________________________________ > DuMux mailing list > [email protected]<mailto:[email protected]> > https://listserv.uni-stuttgart.de/mailman/listinfo/dumux
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