Dear Matrin Thank you very much! It is exactly the problem of "mapping", in my calculation of the drag/lift coefficient, a "mapping" is not added as the first argument to the FEFaceValues constructor. After this fixed, the result looks much better.

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Once again, thanks for your kind help! Best, Howe 在 2017年8月9日星期三 UTC+8下午5:38:57，Martin Kronbichler写道： > > Dear Howe, > > Regarding 1., the main question is whether you added the 'mapping' > variable as the first arguments to all FEValues and FEFaceValues > constructors, to calls to VectorTools::interpolate* and > VectorTools::integrate_difference calls and the like, i.e., all routines > that internally construct an FEValues or FEFaceValues object. There is > defaults for many of those data structures using linear mappings, > MappingQ1, but you don't want to use them but rather the high order > description. > > Regarding 2, I guess you are using a curved boundary description as > explained in step-1? You need to tell the triangulation to use a curved > description. > > Regarding 3, your mesh looks quite good. You would probably want to use a > volume manifold on the whole circular part of the domain, though. And > ideally a TransfiniteInterpolationManifold on the regions where you go from > the circle to the straight ends, but the latter is not yet available in any > of the releases yet, only the github code, and it is not critical and you > should get better results up to degree 3 at least. > > Best, > Martin > > On 09.08.2017 10:06, Howe wrote: > > Dear Martin, > > Thanks for your rapid response. > 1. > The MappingQ is set to be the same as the order of velocity, as is shown > in the following code snippet: > > >> *template <int dim> * >> *NS<dim>::NS (ParameterHandler &prm) * >> *: * >> * parameters (&prm), * >> * degree (prm.get_integer("pressure degree")), * >> * fe( FE_Q<dim>(QGaussLobatto<1>(degree+2)), dim, * >> * FE_Q<dim>(QGaussLobatto<1>(degree+1)), 1), * >> * fe_scalar (FE_Q<dim>(QGaussLobatto<1>(degree+2))), * >> * dof_handler (triangulation), * >> * dof_handler_scalar (triangulation), * >> * mapping (degree+2), * >> * computing_timer (std::cout, * >> * TimerOutput::summary, ** TimerOutput::wall_times)* > > > I am not quite sure whether the computation of the lift/drag in my code is > right, and my implementation is almost the same as the one in this post: > https://groups.google.com/d/msg/dealii/rS6soTb69ig/C4QchAyEGwAJ > The only change is the first line : > > *QGauss<dim-1> face_quadrature_formula(degree+2);* > > > 2. I am using deal.II 8.4.0 now, and I think i am not using manifold > description in my code > > 3. The mesh is shown as follows: > > > <https://lh3.googleusercontent.com/-Vs0s6So28js/WYrCbyok9mI/AAAAAAAABSc/rfs-1D1TA8c71IQZpOEyOoU3C1idNr1DQCLcBGAs/s1600/Image.png> > > > Best, > > Howe > > > 在 2017年8月9日星期三 UTC+8下午3:25:20，Martin Kronbichler写道： >> >> Dear Howe, >> >> How did you run your simulation? From your picture, it appears that a >> higher order method is worse at higher degrees than a lower order method, >> which does not match with my experience. If that were the case, nobody >> would use high orders. However, you need to bring many pieces in place to >> really get to the benefit of the high order method for somewhat more >> complicated examples such as the flow around a cylinder. Here is a list of >> things to look at: >> >> - Do you use a high-order polynomial mapping MappingQ of the same or >> higher degree as the interpolation space? Do you use this mapping in all >> routines that evaluate quantities, such as the usual assembly, the >> computation of the lift/drag, and so on? >> - Do you use a manifold description that extends into the domain? (Look >> into TransfiniteInterpolationManifold.) Without, you will not get more than >> third order convergence. >> - Do you have a good mesh around the area of interest? Flows around >> cylinders tend to be really really sensitive to the mesh quality around the >> cylinder. >> >> For the Navier-Stokes equations around the cylinder, if everything is >> done right one gets significantly improved results in terms of accuracy >> over the number of degrees of freedom up to degree (6,5) >> (velocity,pressure). Beyond that picture is less clear. At least with the >> meshes that we tried in our group it was not worth to go beyond. You can >> have a look a our results in section 5.4 and Figs. 9 and 10 of this >> preprint: >> https://arxiv.org/pdf/1706.09252.pdf >> >> Best, >> Martin >> >> On 09.08.2017 09:01, Howe wrote: >> >> Dear Jaekwang >> >> Have you solved this problem? If yes, Could pls share your solution with >> us? >> I am simulating a steady state flow over a cylinder, and the drag/lift >> coefficient shows an unexpected trend of change as i increase the >> discretization order and refine the mesh. >> >> >> <https://lh3.googleusercontent.com/-Gz5932Zt6e0/WYqvbO3P-4I/AAAAAAAABSM/6hBHn1FO5W0P7X3SPfQ4iyRaldDYzOt3QCLcBGAs/s1600/Image.png> >> >> As is shown in the figure, the Cd increased as the cells increased for >> all the discretization orders, however, for a fixed cells, the Cd decreased >> as the discretization order increased. >> >> In my opinion, to increase the order and refine the mesh should both make >> the approximation more close to the exact solution, thus should have the >> same trend of change. >> >> 在 2016年9月18日星期日 UTC+8下午11:57:16，Jaekwang Kim写道： >>> >>> >>> Hello, I am a starter of dealii and am learning a lot these days with >>> the help of video lectures and tutorial examples. >>> >>> I modified step-22 code (stokes flow code) into my own problem, the flow >>> around sphere. >>> >>> and I intend to evaluate the drag force (which is analytically given by >>> stokes equation) >>> >>> My code reached quite close to the value since the absolute error : >>> abs(drag_calculated-drag_exact)/drag_exact is around 10^(-3) >>> >>> However, I expected that if I input higher 'degree' I will receive more >>> accurate result, but it didn't >>> >>> Obviously Q2 is better than Q1. and Q3 is better than Q2. But Q4 or Q4 >>> is not better than Q2 or Q3? >>> >>> Is there any reason on this? >>> >>> (To be specific, if i say degree 2 , that mean I use (2+1) for velocity, >>> (2) for pressure, and (2+2) for Gauss integral.... >>> >>> >>> Thank you >>> >>> Jaekwang Kim >>> >> -- >> 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+un...@googlegroups.com. >> For more options, visit https://groups.google.com/d/optout. >> >> >> -- > 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+un...@googlegroups.com <javascript:>. > For more options, visit https://groups.google.com/d/optout. > > > -- 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. 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