[GiDlist] quadrilaterals in circles

Moderator: GiD Team

Benjamin Sanderse

[GiDlist] quadrilaterals in circles

Postby Benjamin Sanderse » Tue Dec 19, 2006 1:32 am

Hello all,

I have the following problem: I want to simulate the flow around a cylinder in 3D. The cylinder must be detached from the sides of the domain in order to see edge effects. The code that I am using accepts only hex elements; basically I use quadrilaterals extruded tot a third dimension. The problem now lies in modelling the two ends (circles) of the cylinder, since GiD does not allow me to model them as quads... What is the solution for this?

Benjamin
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abelcs
Posts: 141
Joined: Mon Oct 13, 2014 9:14 am

[GiDlist] quadrilaterals in circles

Postby abelcs » Tue Dec 19, 2006 10:51 am

Hello Benjamin,



You can mesh circles with quadrilaterals using GiD. If you want the mesh to
be structured, the circle must have 4 contour lines, but this kind of meshes
is not “nice” in circles.

The best thing you can do is to mesh the circles using unstructured
quadrilateral. The only restriction for doing this kind of mesh is that each
contour line of the circle must have an even number of elements (divisions).



Regards,



ABEL



__________________________________________________________

Abel Coll Sans

CIMNE - International Center for Numerical Methods in Engineering

Office C2 - C1Building - Campus Nord UPC

Gran Capità s/n, 08034 Barcelona

Tfn: 34 - 93 401 74 03 Fax: 34 - 93 401 65 17

mailto:abelcs at cimne.upc.edu abelcs at cimne.upc.edu

_________________________________________________________

_____

De: gidlist-admin at gatxan.cimne.upc.edu
[mailto:gidlist-admin at gatxan.cimne.upc.edu] En nombre de Benjamin Sanderse
Enviado el: martes, 19 de diciembre de 2006 1:27
Para: gidlist at gatxan.cimne.upc.es
Asunto: [GiDlist] quadrilaterals in circles



Hello all,



I have the following problem: I want to simulate the flow around a cylinder
in 3D. The cylinder must be detached from the sides of the domain in order
to see edge effects. The code that I am using accepts only hex elements;
basically I use quadrilaterals extruded tot a third dimension. The problem
now lies in modelling the two ends (circles) of the cylinder, since GiD does
not allow me to model them as quads... What is the solution for this?



Benjamin

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escolano
Posts: 1627
Joined: Thu Sep 18, 2014 3:31 pm

[GiDlist] quadrilaterals in circles

Postby escolano » Tue Dec 19, 2006 12:16 pm

You can also try the other option pointed by Abel: subdivide the circle in 4-sided structured parts.
I attach an image of two possible patterns. The second one can have acceptable quality.




----- Original Message -----
From: Benjamin Sanderse
To: gidlist at gatxan.cimne.upc.es
Sent: Tuesday, December 19, 2006 1:26 AM
Subject: [GiDlist] quadrilaterals in circles


Hello all,

I have the following problem: I want to simulate the flow around a cylinder in 3D. The cylinder must be detached from the sides of the domain in order to see edge effects. The code that I am using accepts only hex elements; basically I use quadrilaterals extruded tot a third dimension. The problem now lies in modelling the two ends (circles) of the cylinder, since GiD does not allow me to model them as quads... What is the solution for this?

Benjamin
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Benjamin Sanderse

[GiDlist] quadrilaterals in circles

Postby Benjamin Sanderse » Tue Dec 19, 2006 4:31 pm

Thank you all. It indeed worked in 2 dimensions. In 3D it hoewever doesn't seem to work, and I could not figure out why.
I attached my geometry, so maybe you can have a look at it.
As you can see, only half of the cylinder has a volume defined in it. This part is supposed to be fluid.
The other part does not need a mesh inside, as it is the body of the cylinder. Meshing gives an error at the cylindrical volume.
How do you think to solve this?

Benjamin
----- Original Message -----
From: Enrique Escolano
To: gidlist at gatxan.cimne.upc.edu
Sent: Tuesday, December 19, 2006 5:59 AM
Subject: Re: [GiDlist] quadrilaterals in circles


You can also try the other option pointed by Abel: subdivide the circle in 4-sided structured parts.
I attach an image of two possible patterns. The second one can have acceptable quality.




----- Original Message -----
From: Benjamin Sanderse
To: gidlist at gatxan.cimne.upc.es
Sent: Tuesday, December 19, 2006 1:26 AM
Subject: [GiDlist] quadrilaterals in circles


Hello all,

I have the following problem: I want to simulate the flow around a cylinder in 3D. The cylinder must be detached from the sides of the domain in order to see edge effects. The code that I am using accepts only hex elements; basically I use quadrilaterals extruded tot a third dimension. The problem now lies in modelling the two ends (circles) of the cylinder, since GiD does not allow me to model them as quads... What is the solution for this?

Benjamin
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Benjamin Sanderse

[GiDlist] quadrilaterals in circles

Postby Benjamin Sanderse » Tue Dec 19, 2006 4:46 pm

And the attachment....
----- Original Message -----
From: Enrique Escolano
To: gidlist at gatxan.cimne.upc.edu
Sent: Tuesday, December 19, 2006 5:59 AM
Subject: Re: [GiDlist] quadrilaterals in circles


You can also try the other option pointed by Abel: subdivide the circle in 4-sided structured parts.
I attach an image of two possible patterns. The second one can have acceptable quality.




----- Original Message -----
From: Benjamin Sanderse
To: gidlist at gatxan.cimne.upc.es
Sent: Tuesday, December 19, 2006 1:26 AM
Subject: [GiDlist] quadrilaterals in circles


Hello all,

I have the following problem: I want to simulate the flow around a cylinder in 3D. The cylinder must be detached from the sides of the domain in order to see edge effects. The code that I am using accepts only hex elements; basically I use quadrilaterals extruded tot a third dimension. The problem now lies in modelling the two ends (circles) of the cylinder, since GiD does not allow me to model them as quads... What is the solution for this?

Benjamin
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User avatar
abelcs
Posts: 141
Joined: Mon Oct 13, 2014 9:14 am

[GiDlist] quadrilaterals in circles

Postby abelcs » Tue Dec 19, 2006 6:31 pm

Hello,



It seams that you had not assigned compatible meshing data to entities.

Using GiD, hexahedra elements can only be done using structured or
semi-structured volume mesh, so all the volumes must have this kind of
meshes. I send you an example of a possible mesh of your model.



Regards,



ABEL

__________________________________________________________

Abel Coll Sans

CIMNE - International Center for Numerical Methods in Engineering

Office C2 - C1Building - Campus Nord UPC

Gran Capità s/n, 08034 Barcelona

Tfn: 34 - 93 401 74 03 Fax: 34 - 93 401 65 17

mailto:abelcs at cimne.upc.edu abelcs at cimne.upc.edu

_________________________________________________________

_____

De: gidlist-admin at gatxan.cimne.upc.edu
[mailto:gidlist-admin at gatxan.cimne.upc.edu] En nombre de Benjamin Sanderse
Enviado el: martes, 19 de diciembre de 2006 16:32
Para: gidlist at gatxan.cimne.upc.edu
Asunto: Re: [GiDlist] quadrilaterals in circles



And the attachment....

----- Original Message -----

From: Enrique mailto:escolano at cimne.upc.edu Escolano

To: gidlist at gatxan.cimne.upc.edu

Sent: Tuesday, December 19, 2006 5:59 AM

Subject: Re: [GiDlist] quadrilaterals in circles



You can also try the other option pointed by Abel: subdivide the circle in
4-sided structured parts.

I attach an image of two possible patterns. The second one can have
acceptable quality.









----- Original Message -----

From: Benjamin Sanderse mailto:bsanderse at gmail.com

To: gidlist at gatxan.cimne.upc.es

Sent: Tuesday, December 19, 2006 1:26 AM

Subject: [GiDlist] quadrilaterals in circles



Hello all,



I have the following problem: I want to simulate the flow around a cylinder
in 3D. The cylinder must be detached from the sides of the domain in order
to see edge effects. The code that I am using accepts only hex elements;
basically I use quadrilaterals extruded tot a third dimension. The problem
now lies in modelling the two ends (circles) of the cylinder, since GiD does
not allow me to model them as quads... What is the solution for this?



Benjamin

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Benjamin Sanderse

[GiDlist] quadrilaterals in circles

Postby Benjamin Sanderse » Tue Dec 19, 2006 10:01 pm

I see that your mesh is indeed working, but I cannot discover what you changed to make it work. I defined the volume as structured mesh and the front and end circles as unstructured. I still get the error messages that for the circular surface 'all contour lines must have an even number of sides'. The circles have 8 sides and I defined two elements on each side. I do not see why this doesn't work. Can you give me your approach?

Benjamin

----- Original Message -----
From: Abel Coll
To: gidlist at gatxan.cimne.upc.edu
Sent: Tuesday, December 19, 2006 12:12 PM
Subject: RE: [GiDlist] quadrilaterals in circles


Hello,



It seams that you had not assigned compatible meshing data to entities.

Using GiD, hexahedra elements can only be done using structured or semi-structured volume mesh, so all the volumes must have this kind of meshes. I send you an example of a possible mesh of your model.



Regards,



ABEL

__________________________________________________________

Abel Coll Sans

CIMNE - International Center for Numerical Methods in Engineering

Office C2 - C1Building - Campus Nord UPC

Gran Capità s/n, 08034 Barcelona

Tfn: 34 - 93 401 74 03 Fax: 34 - 93 401 65 17

abelcs at cimne.upc.edu

_________________________________________________________


------------------------------------------------------------------------------

De: gidlist-admin at gatxan.cimne.upc.edu [mailto:gidlist-admin at gatxan.cimne.upc.edu] En nombre de Benjamin Sanderse
Enviado el: martes, 19 de diciembre de 2006 16:32
Para: gidlist at gatxan.cimne.upc.edu
Asunto: Re: [GiDlist] quadrilaterals in circles



And the attachment....

----- Original Message -----

From: Enrique Escolano

To: gidlist at gatxan.cimne.upc.edu

Sent: Tuesday, December 19, 2006 5:59 AM

Subject: Re: [GiDlist] quadrilaterals in circles



You can also try the other option pointed by Abel: subdivide the circle in 4-sided structured parts.

I attach an image of two possible patterns. The second one can have acceptable quality.









----- Original Message -----

From: Benjamin Sanderse

To: gidlist at gatxan.cimne.upc.es

Sent: Tuesday, December 19, 2006 1:26 AM

Subject: [GiDlist] quadrilaterals in circles



Hello all,



I have the following problem: I want to simulate the flow around a cylinder in 3D. The cylinder must be detached from the sides of the domain in order to see edge effects. The code that I am using accepts only hex elements; basically I use quadrilaterals extruded tot a third dimension. The problem now lies in modelling the two ends (circles) of the cylinder, since GiD does not allow me to model them as quads... What is the solution for this?



Benjamin
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User avatar
abelcs
Posts: 141
Joined: Mon Oct 13, 2014 9:14 am

[GiDlist] quadrilaterals in circles

Postby abelcs » Wed Dec 20, 2006 11:00 am

Hello,



You have to ensure that the line divisions are compatible.

For example: if you want to mesh one four-sided surface with structured
quadrilateral and you assign 2 and 3 number of divisions to opposite lines
of the surface, GiD will mesh both lines with 3 number of divisions, to make
the mesh compatible. May be this is the reason why your circle lines are
meshed with an odd number of divisions, even if you assign an even number of
it (in your case 2).



A part from that, which GiD version are you using? I recommend you to use
the last official version (8.0.2), because there are some bug fixed from
older versions.



Regards,




ABEL

__________________________________________________________

Abel Coll Sans

CIMNE - International Center for Numerical Methods in Engineering

Office C2 - C1Building - Campus Nord UPC

Gran Capità s/n, 08034 Barcelona

Tfn: 34 - 93 401 74 03 Fax: 34 - 93 401 65 17

mailto:abelcs at cimne.upc.edu abelcs at cimne.upc.edu

_________________________________________________________

_____

De: gidlist-admin at gatxan.cimne.upc.edu
[mailto:gidlist-admin at gatxan.cimne.upc.edu] En nombre de Benjamin Sanderse
Enviado el: martes, 19 de diciembre de 2006 21:50
Para: gidlist at gatxan.cimne.upc.edu
Asunto: Re: [GiDlist] quadrilaterals in circles



I see that your mesh is indeed working, but I cannot discover what you
changed to make it work. I defined the volume as structured mesh and the
front and end circles as unstructured. I still get the error messages that
for the circular surface 'all contour lines must have an even number of
sides'. The circles have 8 sides and I defined two elements on each side. I
do not see why this doesn't work. Can you give me your approach?



Benjamin



----- Original Message -----

From: Abel Coll mailto:abelcs at cimne.upc.edu

To: gidlist at gatxan.cimne.upc.edu

Sent: Tuesday, December 19, 2006 12:12 PM

Subject: RE: [GiDlist] quadrilaterals in circles



Hello,



It seams that you had not assigned compatible meshing data to entities.

Using GiD, hexahedra elements can only be done using structured or
semi-structured volume mesh, so all the volumes must have this kind of
meshes. I send you an example of a possible mesh of your model.



Regards,



ABEL

__________________________________________________________

Abel Coll Sans

CIMNE - International Center for Numerical Methods in Engineering

Office C2 - C1Building - Campus Nord UPC

Gran Capità s/n, 08034 Barcelona

Tfn: 34 - 93 401 74 03 Fax: 34 - 93 401 65 17

mailto:abelcs at cimne.upc.edu abelcs at cimne.upc.edu

_________________________________________________________


_____


De: gidlist-admin at gatxan.cimne.upc.edu
[mailto:gidlist-admin at gatxan.cimne.upc.edu] En nombre de Benjamin Sanderse
Enviado el: martes, 19 de diciembre de 2006 16:32
Para: gidlist at gatxan.cimne.upc.edu
Asunto: Re: [GiDlist] quadrilaterals in circles



And the attachment....

----- Original Message -----

From: Enrique mailto:escolano at cimne.upc.edu Escolano

To: gidlist at gatxan.cimne.upc.edu

Sent: Tuesday, December 19, 2006 5:59 AM

Subject: Re: [GiDlist] quadrilaterals in circles



You can also try the other option pointed by Abel: subdivide the circle in
4-sided structured parts.

I attach an image of two possible patterns. The second one can have
acceptable quality.









----- Original Message -----

From: Benjamin Sanderse mailto:bsanderse at gmail.com

To: gidlist at gatxan.cimne.upc.es

Sent: Tuesday, December 19, 2006 1:26 AM

Subject: [GiDlist] quadrilaterals in circles



Hello all,



I have the following problem: I want to simulate the flow around a cylinder
in 3D. The cylinder must be detached from the sides of the domain in order
to see edge effects. The code that I am using accepts only hex elements;
basically I use quadrilaterals extruded tot a third dimension. The problem
now lies in modelling the two ends (circles) of the cylinder, since GiD does
not allow me to model them as quads... What is the solution for this?



Benjamin

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Benjamin Sanderse

[GiDlist] quadrilaterals in circles

Postby Benjamin Sanderse » Thu Dec 21, 2006 11:12 pm

Hi Abel,

I get your point yes, but still I am not able to get it working myself.
If I define the interior cylinder volume as structured of semi-structured GiD crashes. I am using version 8.0.2, so that should work...?

Benjamin
----- Original Message -----
From: Abel Coll
To: gidlist at gatxan.cimne.upc.edu
Sent: Wednesday, December 20, 2006 4:48 AM
Subject: RE: [GiDlist] quadrilaterals in circles




Hello,



You have to ensure that the line divisions are compatible.

For example: if you want to mesh one four-sided surface with structured quadrilateral and you assign 2 and 3 number of divisions to opposite lines of the surface, GiD will mesh both lines with 3 number of divisions, to make the mesh compatible. May be this is the reason why your circle lines are meshed with an odd number of divisions, even if you assign an even number of it (in your case 2).



A part from that, which GiD version are you using? I recommend you to use the last official version (8.0.2), because there are some bug fixed from older versions.



Regards,



ABEL

__________________________________________________________

Abel Coll Sans

CIMNE - International Center for Numerical Methods in Engineering

Office C2 - C1Building - Campus Nord UPC

Gran Capità s/n, 08034 Barcelona

Tfn: 34 - 93 401 74 03 Fax: 34 - 93 401 65 17

abelcs at cimne.upc.edu

_________________________________________________________


------------------------------------------------------------------------------

De: gidlist-admin at gatxan.cimne.upc.edu [mailto:gidlist-admin at gatxan.cimne.upc.edu] En nombre de Benjamin Sanderse
Enviado el: martes, 19 de diciembre de 2006 21:50
Para: gidlist at gatxan.cimne.upc.edu
Asunto: Re: [GiDlist] quadrilaterals in circles



I see that your mesh is indeed working, but I cannot discover what you changed to make it work. I defined the volume as structured mesh and the front and end circles as unstructured. I still get the error messages that for the circular surface 'all contour lines must have an even number of sides'. The circles have 8 sides and I defined two elements on each side. I do not see why this doesn't work. Can you give me your approach?



Benjamin



----- Original Message -----

From: Abel Coll

To: gidlist at gatxan.cimne.upc.edu

Sent: Tuesday, December 19, 2006 12:12 PM

Subject: RE: [GiDlist] quadrilaterals in circles



Hello,



It seams that you had not assigned compatible meshing data to entities.

Using GiD, hexahedra elements can only be done using structured or semi-structured volume mesh, so all the volumes must have this kind of meshes. I send you an example of a possible mesh of your model.



Regards,



ABEL

__________________________________________________________

Abel Coll Sans

CIMNE - International Center for Numerical Methods in Engineering

Office C2 - C1Building - Campus Nord UPC

Gran Capità s/n, 08034 Barcelona

Tfn: 34 - 93 401 74 03 Fax: 34 - 93 401 65 17

abelcs at cimne.upc.edu

_________________________________________________________


----------------------------------------------------------------------------

De: gidlist-admin at gatxan.cimne.upc.edu [mailto:gidlist-admin at gatxan.cimne.upc.edu] En nombre de Benjamin Sanderse
Enviado el: martes, 19 de diciembre de 2006 16:32
Para: gidlist at gatxan.cimne.upc.edu
Asunto: Re: [GiDlist] quadrilaterals in circles



And the attachment....

----- Original Message -----

From: Enrique Escolano

To: gidlist at gatxan.cimne.upc.edu

Sent: Tuesday, December 19, 2006 5:59 AM

Subject: Re: [GiDlist] quadrilaterals in circles



You can also try the other option pointed by Abel: subdivide the circle in 4-sided structured parts.

I attach an image of two possible patterns. The second one can have acceptable quality.









----- Original Message -----

From: Benjamin Sanderse

To: gidlist at gatxan.cimne.upc.es

Sent: Tuesday, December 19, 2006 1:26 AM

Subject: [GiDlist] quadrilaterals in circles



Hello all,



I have the following problem: I want to simulate the flow around a cylinder in 3D. The cylinder must be detached from the sides of the domain in order to see edge effects. The code that I am using accepts only hex elements; basically I use quadrilaterals extruded tot a third dimension. The problem now lies in modelling the two ends (circles) of the cylinder, since GiD does not allow me to model them as quads... What is the solution for this?



Benjamin
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User avatar
abelcs
Posts: 141
Joined: Mon Oct 13, 2014 9:14 am

[GiDlist] quadrilaterals in circles

Postby abelcs » Fri Dec 22, 2006 9:05 am

Hi Benjamin,



There is a corrected bug in the 8.0.2 version, that will be available in the
next official version. It will be public very soon (today or the next week),
so you will be able to mesh your model.

I thought it was already fixed in the 8.0.2 version, so I’m sorry for have
not telling this to you before.



Thanks for notifying us this irregular behaviour of GiD.



Best regards,




ABEL





__________________________________________________________

Abel Coll Sans

CIMNE - International Center for Numerical Methods in Engineering

Office C2 - C1Building - Campus Nord UPC

Gran Capità s/n, 08034 Barcelona

Tfn: 34 - 93 401 74 03 Fax: 34 - 93 401 65 17

mailto:abelcs at cimne.upc.edu abelcs at cimne.upc.edu

_________________________________________________________

_____

De: gidlist-admin at gatxan.cimne.upc.edu
[mailto:gidlist-admin at gatxan.cimne.upc.edu] En nombre de Benjamin Sanderse
Enviado el: jueves, 21 de diciembre de 2006 23:10
Para: gidlist at gatxan.cimne.upc.edu
Asunto: Re: [GiDlist] quadrilaterals in circles



Hi Abel,



I get your point yes, but still I am not able to get it working myself.

If I define the interior cylinder volume as structured of semi-structured
GiD crashes. I am using version 8.0.2, so that should work...?



Benjamin

----- Original Message -----

From: Abel Coll mailto:abelcs at cimne.upc.edu

To: gidlist at gatxan.cimne.upc.edu

Sent: Wednesday, December 20, 2006 4:48 AM

Subject: RE: [GiDlist] quadrilaterals in circles





Hello,



You have to ensure that the line divisions are compatible.

For example: if you want to mesh one four-sided surface with structured
quadrilateral and you assign 2 and 3 number of divisions to opposite lines
of the surface, GiD will mesh both lines with 3 number of divisions, to make
the mesh compatible. May be this is the reason why your circle lines are
meshed with an odd number of divisions, even if you assign an even number of
it (in your case 2).



A part from that, which GiD version are you using? I recommend you to use
the last official version (8.0.2), because there are some bug fixed from
older versions.



Regards,




ABEL

__________________________________________________________

Abel Coll Sans

CIMNE - International Center for Numerical Methods in Engineering

Office C2 - C1Building - Campus Nord UPC

Gran Capità s/n, 08034 Barcelona

Tfn: 34 - 93 401 74 03 Fax: 34 - 93 401 65 17

mailto:abelcs at cimne.upc.edu abelcs at cimne.upc.edu

_________________________________________________________


_____


De: gidlist-admin at gatxan.cimne.upc.edu
[mailto:gidlist-admin at gatxan.cimne.upc.edu] En nombre de Benjamin Sanderse
Enviado el: martes, 19 de diciembre de 2006 21:50
Para: gidlist at gatxan.cimne.upc.edu
Asunto: Re: [GiDlist] quadrilaterals in circles



I see that your mesh is indeed working, but I cannot discover what you
changed to make it work. I defined the volume as structured mesh and the
front and end circles as unstructured. I still get the error messages that
for the circular surface 'all contour lines must have an even number of
sides'. The circles have 8 sides and I defined two elements on each side. I
do not see why this doesn't work. Can you give me your approach?



Benjamin



----- Original Message -----

From: Abel Coll mailto:abelcs at cimne.upc.edu

To: gidlist at gatxan.cimne.upc.edu

Sent: Tuesday, December 19, 2006 12:12 PM

Subject: RE: [GiDlist] quadrilaterals in circles



Hello,



It seams that you had not assigned compatible meshing data to entities.

Using GiD, hexahedra elements can only be done using structured or
semi-structured volume mesh, so all the volumes must have this kind of
meshes. I send you an example of a possible mesh of your model.



Regards,



ABEL

__________________________________________________________

Abel Coll Sans

CIMNE - International Center for Numerical Methods in Engineering

Office C2 - C1Building - Campus Nord UPC

Gran Capità s/n, 08034 Barcelona

Tfn: 34 - 93 401 74 03 Fax: 34 - 93 401 65 17

mailto:abelcs at cimne.upc.edu abelcs at cimne.upc.edu

_________________________________________________________


_____


De: gidlist-admin at gatxan.cimne.upc.edu
[mailto:gidlist-admin at gatxan.cimne.upc.edu] En nombre de Benjamin Sanderse
Enviado el: martes, 19 de diciembre de 2006 16:32
Para: gidlist at gatxan.cimne.upc.edu
Asunto: Re: [GiDlist] quadrilaterals in circles



And the attachment....

----- Original Message -----

From: Enrique mailto:escolano at cimne.upc.edu Escolano

To: gidlist at gatxan.cimne.upc.edu

Sent: Tuesday, December 19, 2006 5:59 AM

Subject: Re: [GiDlist] quadrilaterals in circles



You can also try the other option pointed by Abel: subdivide the circle in
4-sided structured parts.

I attach an image of two possible patterns. The second one can have
acceptable quality.









----- Original Message -----

From: Benjamin Sanderse mailto:bsanderse at gmail.com

To: gidlist at gatxan.cimne.upc.es

Sent: Tuesday, December 19, 2006 1:26 AM

Subject: [GiDlist] quadrilaterals in circles



Hello all,



I have the following problem: I want to simulate the flow around a cylinder
in 3D. The cylinder must be detached from the sides of the domain in order
to see edge effects. The code that I am using accepts only hex elements;
basically I use quadrilaterals extruded tot a third dimension. The problem
now lies in modelling the two ends (circles) of the cylinder, since GiD does
not allow me to model them as quads... What is the solution for this?



Benjamin

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