Hi Victor, Thank you for the answer. I do not think Krzysztof question is about enforcing incompresibilty per se, but rather about, what seems to be an inconsistency in the initialization of the time stepping with regard to the pressure boundary condition. Namely, higher order IMEX method is not self starting and needs to be initiated by a multistage method. It seems that during this couple of steps there might be an inconsistency with regard to which we ask this question. Krzysztof has been looking into this, and his observation are outlined in the pdf. He suggests that pressure boundary condition (eq. 4 of the pdf) and the discrete in time (8) variant are consistent for a developed time stepping IMEX, but not for the initialization step. So the question is, does it matter, or is it that we do not see the equivalence? Best regards, Stan *Faculty of Power and Aeronautical Engineering* Nowowiejska 24 Str. 00-665 Warsaw, Poland phone +48 (22) 234 75 23 <https://www.pw.edu.pl/engpw> On 14.10.2025 15:16, Ballester Ribo, Victor wrote:
Hi Krzysztof,
Nektar++ doesn't enforce incompressibility exactly in the Velocity Correction Scheme. It's chosen like this in the splitting error. You can check that with any run you already have and the postprocessing utility FieldConvert to get the divergence of your field.
FieldConvert -m divergence mesh.xml field.fld field_div.fld
Hopefully if the constant in front is not very big it should be of the order of TimeStep^ORDERSCHEME.
With regards to the pressure BCs, the components of the velocity that appear in the equation are extrapolated as well, so expect another O(TimeStep^ORDER) from there again.
I am not sure whether this solves your concerns, Best,
------------------------------------------------------------------------ *From:* nektar-users-bounces@imperial.ac.uk <nektar-users-bounces@imperial.ac.uk> on behalf of Michałowski Krzysztof (STUD) <krzysztof.michalowski.stud@pw.edu.pl> *Sent:* 14 October 2025 12:32 *To:* nektar-users <nektar-users@imperial.ac.uk> *Subject:* [Nektar-users] Pressure boundary conditions for velocity correction scheme
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Hello,
I am a student at Warsaw University of Technology and I will be using Nektar++ for my masters thesis. I have a question about pressure boundary conditions for velocity correction scheme. To ask this question i had to write down some formulas that is why it was more conviniant to attache it to this message as a pdf document.
Best Regards, Krzysztof Michałowski
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