[CIG-SHORT] Direction of traction-normal for Neumann BC
Brad Aagaard
baagaard at usgs.gov
Thu Jun 19 07:56:17 PDT 2014
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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