Question about vector correction function in PyFR.

[Kiny Wan]

Hello everyone,

        I recently read the book about high-order flux reconstruction schemes and found the vector correction function for triangle element. I would like to ask a question about how to get these vectors in PyFR? The references include the Ph.D. thesis of P. Castonguay and the chapter 10 of F.D. Witherden, P.E. Vincent and A. Jameson.

Regards

Kiny

[Freddie Witherden]

Hi,

During an FR step one only needs the divergence of these functions.  Moreover, it turns out to be simpler to directly compute the divergence of these functions.  This is the approach taken by PyFR.

Regards, Freddie.

On 18 Jul 2020, at 02:28, Kiny Wan <wlc...@gmail.com> wrote:

Hello everyone,

        I recently read the book about high-order flux reconstruction schemes and found the vector correction function for triangle element. I would like to ask a question about how to get these vectors in PyFR? The references include the Ph.D. thesis of P. Castonguay and the chapter 10 of F.D. Witherden, P.E. Vincent and A. Jameson.

Regards

Kiny

<correction function.jpg>

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<correction function.jpg>

[Vincent, Peter E]

Hi Kiny,

As Freddie says, PyFR only deals with the divergence of these correction functions, and not the vector correction functions themselves.

The DG variants are the default coded into PyFR.

To try others you could adopt an approach similar to that which Brian adopted here for tensor product elements:

https://www.sciencedirect.com/science/article/pii/S0021999116304557

in which I believe he modified the code for calculating the m3 matrix to read from a file instead of calling gbasis_at (there should be a patch in the Supplementary Material).

One warning about this approach, is that the m3 coefficients you read from a file will have to have been generated in the context of a specific set of solution points, so if you run with anything but those solutions points it will lead to problems! I guess another approach would be to generalise gbasis_at.

Thanks

Peter 

Dr Peter Vincent MSci ARCS DIC PhD FRAeS
Reader in Aeronautics and EPSRC Fellow
Department of Aeronautics
Imperial College London
South Kensington
London
SW7 2AZ
UK

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[Kiny Wan]

Thank you Freddie. I finally understand what you mean. It is more convenient to use the divergence of correction function as they are fixed form. Regards Kiny

[Kiny Wan]

Hi Peter, 

        Thank you very much. I found the 'patch.patch' in the supplementary material as follow. It replaces gbasis_at with the python operation of loadtxt for specific degree of polynomial. I will study the theory in this paper.

Regards

Kiny

From 44d8c84475255aed777c4fd728fcca2feaa35620 Mon Sep 17 00:00:00 2001

From: brian` <vermeir...@gmail.com>

Date: Mon, 7 Mar 2016 10:54:52 +0000

Subject: [PATCH] Load custom correction functions.

---

 PyFR-1.1.0/pyfr/shapes.py | 3 ++-

 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/PyFR-1.1.0/pyfr/shapes.py b/PyFR-1.1.0/pyfr/shapes.py

index 1a05c8c..54f59dd 100644

--- a/PyFR-1.1.0/pyfr/shapes.py

+++ b/PyFR-1.1.0/pyfr/shapes.py

@@ -98,7 +98,8 @@ class BaseShape(object):

 

     @lazyprop

     def m3(self):

-        m = self.gbasis_at(self.upts)

+        m = np.loadtxt('./hex.dat')

+        #m = self.gbasis_at(self.upts)

 

         if 'surf-flux' in self.antialias:

             fp = [_proj_l2(self._iqrules[kind],

-- 

1.9.1