[CIG-SHORT] Direction of traction-normal for Neumann BC

[Brad Aagaard]

Satoshi,

The Neumann BC is intended to be applied to an external boundary. For a 
spherical pressure source, the domain should not include the material 
inside the sphere (it needs to be a cavity). This will result in a 
consistent normal direction for the boundary.

If the spherical boundary is all one surface, then you can still run 
into problems when PyLith initializes the boundary. It may find 
horizontal normal directions. This means the default way it uniquely 
defines the two tangential directions breaks down. The workaround is to 
subdivide the surface into quadrants so that you can use a user-defined 
up-direction to get consistent directions tangential and normal 
directions for the Neumann BC. Attached is a small magma chamber example 
that illustrates this.

We are working on a more detailed magma chamber and dike example for a 
workshop next week and we will create an examples section under PyLith 
User Resources (http://wiki.geodynamics.org/software:pylith:start) in 
the next week and post it there.

Regards,
Brad


On 06/19/2014 02:09 AM, Satoshi Okuyama wrote:
> Hello,
>
> Recently I started using pylith and I already love it. However, I have
> an question about Neumann boundary condition;
>
> What determines the direction of positive traction-normal?
>
> or
>
> What determines the order of the vertices when pylith construct faces
> from a group of vertices for boundary condition?
>
>
> Here is my story,
>
> I am trying to simulate the deformation caused by a pressure source. I
> created a mesh with spherical source and put all the vertices on source
> surface into a group, then applied Neumann BC with just traction-normal.
>
> However, the deformation of the source was far from isotropic. I checked
> the initial traction and found that deflation (traction toward source
> center) is applied to some faces, while inflation is applied to the others.
>
> Following is an example of initial-traction output. I placed 5 vertices
> on a plane of z=0 and formed 4 triangle face. Then I applied +1Pa of
> traction-normal to this group.
>
> #######################################################################
> # vtk DataFile Version 2.0
> Simplicial Mesh Example
> ASCII
> DATASET UNSTRUCTURED_GRID
> POINTS 5 double
> -1.000000e+00 -1.000000e+00 0.000000e+00
> 1.000000e+00 -1.000000e+00 0.000000e+00
> 1.000000e+00 1.000000e+00 0.000000e+00
> -1.000000e+00 1.000000e+00 0.000000e+00
> 0.000000e+00 0.000000e+00 0.000000e+00
> CELLS 4 16
> 3  2 1 4
> 3  3 0 4
> 3  3 2 4
> 3  4 1 0
> CELL_TYPES 4
> 5
> 5
> 5
> 5
> CELL_DATA 4
> VECTORS initial_traction double
> 0.000000e+00 0.000000e+00 -1.000000e+00
> 0.000000e+00 0.000000e+00 1.000000e+00
> 0.000000e+00 0.000000e+00 -1.000000e+00
> 0.000000e+00 0.000000e+00 -1.000000e+00
> #######################################################################
>
> As you see, 2nd cell (or face) receives traction of (0,0,1) while other
> cells receives (0,0,-1). I noticed that if I consider 2 vectors - 1st
> vertex to 2nd, and 1st to 3rd - the direction of the traction vector is
> equal to the cross product of them.
>
> cell #1:
>    v1: #2 -> #1 = ( 0,-2,0)
>    v2: #2 -> #4 = (-1,-1,0)
>    v1 x v2 = (0,0,-2)
>
> cell #2:
>    v1: #3 -> #0 = ( 0,-2,0)
>    v2: #3 -> #4 = ( 1,-1,0)
>    v1 x v2 = (0,0,2)
>
> One step closer to the answer, I believe. But I have no idea how this
> order is determined. The order of the vertices for 2nd cell is 3-0-4,
> not 3-4-0. But why?
>
>
> Regards,
> ----
> Satoshi Okuyama
> _______________________________________________
> CIG-SHORT mailing list
> CIG-SHORT at geodynamics.org
> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>

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