Dear Oded, I believe that Wolfgang has answered your question in much more detail and much more precision than I would have, so I think that there's no need for me to elaborate on further on what I said.
Regards, J-P On Monday, December 5, 2016 at 5:47:17 PM UTC+1, Oded Yaakobi wrote: > > Hi Wolfgang and Jean-Paul, > > > > It seems that one of Wolfgang’s replies to me was not shared through the > user group, so I forward it here. My response is listed below it. > > > > > > *On 12/2/16, 6:18 PM, "Wolfgang Bangerth" wrote:* > > > > > > Oded, > > > > *I know that the typical treatment of the interface matching conditions is* > > *along the lines that you noted. However, it is not clear to me how to > follow* > > *these guidelines in the particular case that I am working on, which is* > > *described in the file that I attached to my previous email. In > particular, in* > > *my case,* > > > > > > > > *a) The matching conditions involve gradients of velocity and pressure, > and* > > *not just the velocity and pressure fields.* > > > > If it doesn't fit into the weak form, and if it isn't easily described as > > constraints on degrees of freedom (as we do for Dirichlet values) then I > don't > > know either. What do others who have published on these models do? > > > > > > *b) The matching conditions involve time-dependent fields, so probably > the* > > *explicit form of the constraints has to be updated each time step.* > > > > > > > > *In order to address point a), I thought that maybe I should define > additional* > > *degrees of freedom that correspond to the components of each one of the* > > *gradient terms that appear in my matching conditions (e.g. for the > pressure* > > *gradient add DOFs P_i_x, P_i_y and P_i_z). I would then define the > constraints* > > *with respect to those new DOFs, and would also have to assemble the* > > *corresponding equations (e.g. P_i_x = dP_i/dx).* > > > > Correct. You need to update the ConstraintMatrix object in every time step. > > > > Best > > W. > > > > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% > > > Wolfgang: > > I am working on generalizing a model that originally described only the > interior domain by the equations that I wrote on my Friday’s notes. I am > not familiar with anyone who solved the combined set of equations for the > interior and exterior domains. However, a simpler problem should be common > in other situations where the droplet is made of a single phase. In these > cases, a matching condition in the form of Eq. 10 in my notes should be > satisfied (with \Psi=0). In recent days I have surveyed the literature to > learn how people deal with these situations, but still haven’t found an > answer. > > > > Jean-Paul: > > I don’t understand exactly what you have suggested. Could you please > elaborate more on how would you impose a matching condition such as Eq. 10 > in a weak sense? > > > Best, > > Oded > > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
