Node ordering trianlges for Flux Reconstruction

General
1

Hi. Does the flux reconstruction approach on triangles require a specific node ordering? Consider two neighboring elements (A & B) with the nodes numbered as follows:

A                B
3                3____2
|\                \   |
| \                \  |
|  \                \ |
|_ _\                \|
1    2                1

A               B
3                2____1
|\                \   |
| \                \  |
|  \                \ |
|_ _\                \|
1    2                3

Element “A” is a scaled version of the reference right triangle in both cases. In the first case, the physical hypotenuse for element “B” is mapped to the vertical edge of the reference right triangle, while in the second case it is mapped to the hypotenuse in the reference space. Does this difference matter? I’m asking because the correction functions (hence the flux divergence) are defined in reference space and the (r,s) coordinates are different for these scenarios [Williams et. al. 2013, JCP, 250, 53-76].

Hope the question was clear. Thanks!

cheers,

Kunal Puri

2

Hi Kunal,

No, it does not matter. The Jacobian factors at the solution and flux
points account for the mapping and so there is no need for the two
vertices which represent the hypotenuse in physical space to also
represent it in reference space.

Regards, Freddie.

3

Hi Kunal,

In PyFR we always assume that elements can be curved hence giving rise
to spatially varying Jacobian factors inside of an element and hence
it can be different at the flux points to the solution points. You
are correct in that if the triangles (or tetrahedra) are straight
sided that the Jacobian factors are constant.

Regards, Freddie.