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
>>
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