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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