scalar-quadrangle-value in Gmsh's ASCII post-processing file

[Robert Jurjevic]

Dear Jean-Francois,

Thank you very much for your help.

Jean-Francois wrote>
So, when you draw, let's say one quadrangle, you first split it into 2 triangles and use your quadrilateral interpolation at points, Then, if your solution is higher order, you split recursively the triangles into 4 triangles, the recursion stops when your solution is sufficiently linear on the actual triangle.

Actually, I will first divide my 4-node (black nodes) quadrangular finite element into four 4-node quadrangles (figure 1) with five new nodes (white nodes) in which I will calculate the pressure using 4-node quadrangular finite element interpolation.

Figure 1: 4-node quadrangular finite element with four new 4-node quadrangles.

Then, I will calculate the difference between linear and 4-node quadrangular finite element interpolated pressure values in red nodes (see figure 2).

Figure 2: 4-node quadrangular finite element with four new 4-node quadrangles. Red nodes are nodes in which we calculate the difference between linear and 4-node quadrangular finite element interpolated pressure values.

If the difference (for all red nodes in figure 2) is not small enough (the difference will be compared to the pressure change on the element) the subdivision should continue as shown in figure 3, where again we calculate the difference between linear and 4-node quadrangular finite element interpolated pressure values in red nodes.

Figure 3: 4-node quadrangular finite element with sixteen new 4-node quadrangles. Red nodes are nodes in which we calculate the difference between linear and 4-node quadrangular finite element interpolated pressure values.

If the difference (for all red nodes) is small enough (say, that it was in figure 3) there is no need for further subdivisions and we are going back to a previous subdivision and form 3-node triangles as shown in figure 4.

Figure 4: Final triangulation of 4-node quadrangular finite element. White nodes are nodes in which we calculate 4-node quadrangular finite element interpolated pressure values.

I intend to write an ANSI C program which will for every accept scalar-quadrangle-value in the input ASCII file generate a corresponding scalar-triangle-value-s in the ASCII output file.

I do not know when I will start working on this, but if I will ever and if I finish the program I will pass the C source to you.

Nevertheless in my opinion a proper way to do it is to implement the support to scalar-quadrangle-value into Gmsh (imagine that you want to zoom something to extremes, etc.).

Thank you.

Yours sincerely,

Robert Jurjevic

----- Original Message ----- 
From: <remacle at scorec.rpi.edu>
To: "Robert Jurjevic" <robert.jurjevic at bhead.co.uk>
Cc: "christophe geuzaine" <Christophe.Geuzaine at ulg.ac.be>
Sent: Tuesday, March 13, 2001 2:18 PM
Subject: Re: scalar-quadrangle-value in Gmsh's ASCII post-processing file


> Hello Robert,
> 
> >
> > Thank you for developing Gmsh!
> >
> 
> You're welcome.
> 
> > My name is Robert Jurjevic and some time ago I wrote a solver for a
> > classical fluid mechanics system of partial differential equations modelling
> > two-dimensional stationary incompressible Newtonian fluid flow.
> >
> > I tried the solver on classical examples of driven cavity laminar flow,
> > laminar flow past a cylinder and a laminar flow past a symmetric NACA
> > airfoil.
> >
> > I used 2D 8-node superparametric (pressure) and isoparametric (velocity)
> > quadrilateral finite elements.
> >
> > Pre- and post-processing has been handled using I-DEAS Finite Element
> > Modelling software running on an HP UNIX workstation.
> >
> > Now when there is a Gmsh, I thought that I could produce a coloured picture
> > of a NACA airfoil pressure field on my PC.
> >
> > I kindly beg you if you could answer the following questions. Thank you.
> >
> 
> Yes, I use here high order finite elements for compressible 3d flows, gmsh
> can display everything but the only primitives are simplices (points,
> lines, triangles, tetrahedron).
> 
> For displaying higher order
> interpolations, we use a recursive algorithm. First, you must undesrtand
> that triangles that you display in gmsh are not s mesh, they may be
> completely disconnected even overlapping (I do not say that it's
> recommended). So, when you draw, le's say one quandrangles, you first
> split it ito 2 triangles and use your quadrilateral interpolant at
> points
> 
> (-1,-1), (-1,1), (1,1) for the first triangle
> (1,1) , (1,-1), (-1,-1) for the second triangle
> 
> Then, if your solution is higher order, you split recursively the
> triangles into 4 triangles, the recursion stops when your solution is
> sufficiently linear on the actual triangle. Look at the attachement, this
> is a very classical example of a supersonic flow (splitted-quads.gif). The
> image shows the subdivision.
> 
> In the other example (iso.jpg), I splitted hexaedron into tetrahedron,
> then recurse.
> 
> 
> > QUESTIONS
> >
> > 1. Is there a scalar-quadrangle-value equivalent of the
> > scalar-triangle-value in the Gmsh ASCII post-processing file. The pressure
> > in my examples is calculated using 2D 8-node superparametric quadrilateral
> > finite elements, but approximation with 2D 4-node isoparametric
> > quadrilateral finite elements will do fine. I know that I can approximate a
> > 2D 4-node isoparametric quadrangle finite element with two 2D 3-node
> > isoparametric triangular finite elements, but I would like to avoid that
> > (extra work and the error).
> 
> No, look below.
> 
> >
> > 2. Do you intend to implement the support for 2D 8-node isoparametric finite
> > elements (for both pre- and post-processing)? If you introduce something
> > like vector-quadrilateral8-value I would be able to present the velocity
> > field (variable length arrows i presume).
> >
> 
> 
> No.
> 
> > If I manage to produce the colourful picture of pressure field for the flow
> > around the airfoil I will send it (the picture or the data to generate the
> > picture) to you.
> >
> 
> Thank you very much. Moreover, we are actually developping plugin
> capabilities for gmsh, if you want to plug your software on gmsh, we can
> give you the material (i.e. source code of the core).
> 
> Jean-Francois.
> 
> 
> > In fact the sole purpose of producing the pressure picture is due to its
> > aesthetic value and I regard it as a peace of scientific art.
> >
> > Yours sincerely,
> >
> > Robert Jurjevic
> >
> >
> 


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