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:

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> *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 <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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