Coordintes transformation for pyramides

General
1

Dear all,

My name is Antonio Garcia-Uceda, and I’m working on implementing a FR algorithm for hybrid meshes.

I’m currently extending my FR method to pyramides, but I’m having troubles to come up with an expression of shape functions to transform from, let’s say a reference pyramide of vertexes (-1,-1,-1), (-1,1,-1), (1,1,-1), (1,-1,-1), (-1,-1,1), to a real pyramide of arbitrary vertexes.

I’d like to provide me with some info if you have already fully devised the FR method for pyramides.

Many thanks in advance,

Best regards,
Antonio

2

In PyFR we never construct these expressions explicitly. Everything we
need can be obtained by constructing suitable nodal bases and then
evaluating them at the right places; see shapes.py in PyFR.

Regards, Freddie.

3

Hi Freddie,

I actually meant the transformation from the reference to the real element, in order to compute Jacobian matrix at the solution points.

Are you telling me that you also compute this transformation through the transformation from modal to nodal basis?

Best regards,
Antonio

4

Hi Antonio,

Thanks for your interest in PyFR.

All nodal basis functions used in PyFR are defined ‘implicitly’ via the definition of i.) a nodal point set and ii.) a modal orthonormal basis for the element in question (coefficients for the expansion of each nodal basis function, in terms of the modal orthonormal basis functions, can then be obtained).

This is therefore the approach used to obtain nodal shape functions.

Hence to define nodal shape functions for a pyramid you would beed to specify i.) a nodal point set and ii.) a modal orthonormal basis for the pyramid. I have not looked into this myself in detail yet.

Cheers

Peter