# [CIG-MC] Zero shear stresses with free-slip boundary conditions

Eh Tan tan2 at geodynamics.org
Wed Jan 21 12:16:41 PST 2009

```Hi C.S.,

Here is the stress vs distance plot at step 0. The shear stress (xy
component) at x=z=0.5 is plotted. The shear stress decreases toward 0 as
y approaches 0 and 1.

The shear stress is not exactly zero in the plot. The slope of the curve
changes near the boundary, which is caused by interpolation. The stress
is computed on the elements and then interpolated to the nodes. The
interpolation is less accurate at the boundary nodes.

If you really care about boundary stress, you need to apply additional
correction, like the correction at line 439 in Topo_gravity.c
tpg[snode] = -2 * SZZ[node] + SZZ[node - 1];
Here, tpg is the non-dimensional dynamic topography at surface, which is
the same as -SZZ at the boundary node. The correction is to add
(SZZ[node0] - SZZ[node1]) to SZZ[node0], where node0 is the boundary
node and node1 is the neighboring node in the normal direction, is this
case, right below node0.

After the correction, the plot becomes:

Now the boundary stress is indeed very close to zero (1e-3).

Cheers,

Eh

Shijie Zhong wrote:
> Dear Mr. Natarajan,
>
> Eh is probably out of town at the moment, and I would be happy to answer your question.
>
> Can you please provide more information? 3D cartesian or regional spherical models? Generally speaking, shear stresses are non-zero numerically at the free-slip boundaries, but if you plot them against the distance from the boundaries, you should see that the stresses decrease towards zero rapidly as the distance decreases.
>
> To reduce the email traffic, you can send your follow-up questions to me and Eh.
>
> Cheers,
>
> Shijie
>
> Shijie Zhong
> Department of Physics
> University of Colorado at Boulder
> Boulder, CO 80309
> Tel: 303-735-5095; Fax: 303-492-7935
>
>
> ---- Original message ----
>
>> Date: Thu, 8 Jan 2009 23:03:50 -0800 (PST)
>> From: "C.S Natarajan" <natarajan at geology.ucdavis.edu>
>> Subject: [CIG-MC] Zero shear stresses with free-slip boundary conditions
>> To: cig-mc at geodynamics.org
>>
>> Hello everybody,
>>     I was wondering if anybody has outputted the shear stresses from
>> Citcom-CU and actually seen that the free-slip boundary condition
>> gives 0 shear stresses. I was trying to run the sample input file
>> provided from the distribution version and output the stresses. I am
>> getting non-zero shear stresses on the vertical faces. I'm wondering
>> what I might be doing wrong. The only code I had to add was a routine
>> to output stresses (calculated in Topo_gravity.c) in Output.c
>>
>>
>> C.S.N
>>
>> _______________________________________________
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>>
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--
Eh Tan
Staff Scientist
Computational Infrastructure for Geodynamics
2750 E. Washington Blvd. Suite 210
(626) 395-1693
http://www.geodynamics.org

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