Thank you for the help. I think that has the pretty much sorted out for me. One additional question: On this test problem people also like to know the pressure drop across the obstacle. This basically involves calculating the pressure at two points in the mesh and finding their difference. I see in step 13 this can be done by hoping that the points you need to evaluate are vertices of the mesh. Is there a more general solution--or a way to ensure a certain point is in the mesh? FYI I'm using the very helpful builtin meshing scheme for this problem: GridGenerator::channel_with_cylinder()
Thanks, Kyle On Monday, September 27, 2021 at 6:24:57 PM UTC-4 Wolfgang Bangerth wrote: > On 9/27/21 1:43 PM, Kyle Schwiebert wrote: > > I'm trying to replicate the simulation described in this paper > > < > https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwias-berlin.de%2Fpeople%2Fjohn%2FELECTRONIC_PAPERS%2FJoh04.IJNMF.pdf&data=04%7C01%7CWolfgang.Bangerth%40colostate.edu%7Ce97881b432a742a2b53008d981ef1a37%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637683686653742835%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=dDqBEMcMDHgOSMr4G2McKiWUmifKo5sSZpc3ReFfUQ8%3D&reserved=0>. > > > > How could I compute the integrals in equations 4 and 5? I'm sure it's > > covered in the tutorial, but I couldn't find it after searching in > > several different steps in the tutorial. Could someone please point me > > to an example in the tutorials where this type of computation with a > > computed solution? The only examples I could find seem to only discuss > > computing L2, or H1 errors with a special function that avoid manually > > computing the integral. Is the easiest thing to do as is done in the > > matrix assembly? > > Kyle, > in essence you just have to loop over all cells and integrate up the > quantity you have in the formula for a given choice of v_l and v_d. This > works in a similar way to this example here where we compute the angular > momentum: > > > https://github.com/geodynamics/aspect/blob/master/source/simulator/nullspace.cc#L357-L459 > > > > Finally, how would one initialize the vectors v_l and v_d? Could it be > > done easily with an appropriate AffineConstraints object? > > As long as you satisfy the boundary conditions, it's your choice. So you > could, for example, start with a zero vector, evaluate boundary values > as indicated on the boundary in question, and then just go through the > constraints you get as a result and apply them to your zero vector (via > AffineConstraints::distribute(), applied to the zero vector). That would > probably be what I'd do. > > Or you just take v_l/v_d as functions that are analytically described > (i.e., that are not finite element functions to begin with). > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: [email protected] > www: http://www.math.colostate.edu/~bangerth/ > -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/161d3d21-836f-43bf-b751-6da7de2a451dn%40googlegroups.com.
