Data location in high order cells and calculation of dimensionless wall normal distance

General
1

Dear developers and dear fellow pyFR users,
I have a few questions concerning the data location in high order cells as present in pyFR and the calculation of the dimensionless wall normal distance (Let’s call it y+ from this point on) accordingly.

  1. Calculation of y+
    To calculate the y+ value for the first cell, I need it’s dimensioned length normal to the wall.
    Am I correct, that since pyFR subdivides every cell further into solution points according to the order of the polynomial solution basis, the real y+ value would depend on the location of the closest solution point next to the wall and thus decrease with increasing polynomial order. Or does the distance from the wall to the first solution point only change marginally and an increase of the polynomial order only boosts the resolution in the center of the cell?
    In consequence do I need to respect wall normal resolution guidelines imposed by the stream’s velocity already by the raw mesh or is it sufficient if the desired resolution is only achieved for a certain polynomial order?

  2. Subdivision option of the pyfr export funcionality
    Another issue I’d like some clarification on is the subdivision option of the vtu export functionality in pyFR. From the user guide I read that the raw mesh gets divided equally spaced depending on the integer provided to the option. It was not clear for me in the first place, whether the option -d 1 corresponds to the one-time division of a raw cell in 2 parts in every spatial direction or if it corresponds to the number of subdomains (The latter seems to be the case).
    I would also like to know how the interpolation of the data at these subdivision points works: Is it linear interpolation between solution points or evaluation of the solution polynomial?
    At last, do you have a recommendation what level of subdivison is reasonable for a certain order?

Best regards,
Hendrik

2

Hi Hendrik,

Thanks for your interest in PyFR.

See inline below:

  1. Calculation of y+
    To calculate the y+ value for the first cell, I need it’s dimensioned length normal to the wall.
    Am I correct, that since pyFR subdivides every cell further into solution points according to the order of the polynomial solution basis, the real y+ value would depend on the location of the closest solution point next to the wall and thus decrease with increasing polynomial order.

Yes.

Or does the distance from the wall to the first solution point only change marginally and an increase of the polynomial order only boosts the resolution in the center of the cell?

No.

In consequence do I need to respect wall normal resolution guidelines imposed by the stream’s velocity already by the raw mesh or is it sufficient if the desired resolution is only achieved for a certain polynomial order?

The latter.

  1. Subdivision option of the pyfr export funcionality
    Another issue I’d like some clarification on is the subdivision option of the vtu export functionality in pyFR. From the user guide I read that the raw mesh gets divided equally spaced depending on the integer provided to the option. It was not clear for me in the first place, whether the option -d 1 corresponds to the one-time division of a raw cell in 2 parts in every spatial direction or if it corresponds to the number of subdomains (The latter seems to be the case).

The latter.

I would also like to know how the interpolation of the data at these subdivision points works: Is it linear interpolation between solution points or evaluation of the solution polynomial?

The latter.

At last, do you have a recommendation what level of subdivison is reasonable for a certain order?

It really depends on what you want to do with the sub-divided data.

Regards

Peter

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