# [aspect-devel] internal velocity boundary conditions

Magali Billen mibillen at ucdavis.edu
Thu May 14 14:27:20 PDT 2015

```Hello Timo, Wolfgang, Jonathan and anyone else interested in this question.

So, based on Wolfgang’s response, I know that I am not (yet) at the level of being
able to implement the internal velocity boundary conditions, but it is good to know that
there is a way of doing this.

In the mean time, I would like to ask Timo if he would be willing to share how to
switch off Stokes and run with fixed velocities everywhere.

I met with my student Scott today and we think we’ve come up with a way to define the
velocity everywhere - there are still some issues we will need to work out but Scott
will be at the Hackathon and this will be the primary thing that he will work on.

One of the issues with defining the velocities everywhere is that  we will need to use a non-uniform grid for the fully-dynamic 3D models (that is higher resolution near the slab/wedge and much coarser mesh in the lower mantle and out near the edges of the boundary), and there’s not an easy way to define the velocities on a non-uniform grid.  We will basically assign the velocities as a “2-D” corner flow solution in which the corner-dip changes as a function the local dip on the slab. We will align the mesh so that the trench is roughly parallel with one mesh direction, then the corner flow will be aligned along the other mesh direction (this is exactly what I did for my Tonga-PhD models).

So, I’ll share the outline of the steps we came up with for doing this  with you all, and if you have
as its tested.
-Magali

Plan for making initial 3D slab thermal structure:
1. Decide on finest grid size that will be needed in the actual instantaneous dynamic model.
2. Outside of Aspect take slab surface location and interpolate to the spacing at the finest grid size.
3. In Aspect
- read in slab surface location SSL - (lon, lat, dep).
- initialize a uniform mesh at the finest grid spacing.
- using the SSL
a. define the distance (in the latitude direction) from the slab at each depth. Some care is needed here for
planes of the mesh that are to the sides of the slab and below.  For these points we  just extend the slab
surface at each depth out to the side of the model domain, and similarly for the below the slab to either side of
the slab, we will extrapolate)
b. (only needs bounds of SSL for this) define the corner-velocity for each point in the mesh as either the
subduction velocity, or a 	tapered fraction of Vsub to the sides (taper to zero or a small value over a few
hundred kilometers).
c. define the slab dip at each depth and latitude, for each point
- Now each point in the grid knows its distance from the corner, its corner-flow-velocity and its local slab dip.
The analytical solution for the corner flow can now be used to define the velocity at each point in the grid.
- define temperature boundary conditions and initial temperature (half-space cooling model that varies with lat,lon 		(also need to read in ascii grid with ages for this step).
- As a last step before running the “kinematic” simulation, we would like to use the AMR-mesh coarsening to coarsen the mesh using the velocity gradient of the prescribed velocity field (CAN WE DO THIS??). We think this step is needed because once we get the temperature result, we want to restart with an instantaneous calculation with a fixed mesh. We would like this mesh to have high resolution around the slab (non-linear rheology) but do not need this resolution in the lower mantle or out toward the edges.
- Run kinematic model for fixed time.
- Restart as dynamic model.

On May 12, 2015, at 6:45 PM, Timo Heister <heister at clemson.edu> wrote:

> Magali,
>
> this might not quite be what you want, but my student Ryan just
> implemented a feature where you can turn off solving for the Stokes
> system and supply a given velocity and pressure in the whole domain.
> So, if you are able to describe the velocity as a function of the
> location, you can run your model like this for a certain amount of
> time before you snapshot and switch to a normal computation where
> velocity is driven by temperature differences again.
>
> Internal boundary conditions are a bit more complicated, especially
> because you need to be careful to pose them in a compatible way.
>
> On Tue, May 12, 2015 at 8:49 PM, Jonathan Perry-Houts
> <jperryh2 at uoregon.edu> wrote:
>> I actually had this on my list of hackathon items as well. It would be
>> very useful.
>>
>> On 05/12/2015 05:46 PM, Thorsten Becker wrote:
>>> Likewise not at the hackathon myself, but this exact application (for
>>> the Tohoku setting) would be of great interest to my group as well...
>>>
>>> Thanks!
>>>
>>> Thorsten W Becker
>>> geodynamics.usc.edu <http://geodynamics.usc.edu/~becker>
>>>
>>> On Tue, May 12, 2015 at 5:43 PM, Magali Billen <mibillen at ucdavis.edu
>>> <mailto:mibillen at ucdavis.edu>> wrote:
>>>
>>>    Hello Everyone,
>>>    Unfortunately I’m not going to make it to Hackathon to ask this
>>>    question in person, but this way everyone
>>>    can read (ignore?) and hear or contribute to the response.
>>>
>>>    The short form of my question is: Is it possible to define
>>>    “internal” velocity boundary conditions in Aspect: that is
>>>    can I fix the velocity at nodes inside the model domain? If the
>>>    answer is yes, can someone comment on the basic steps
>>>    that would be needed (e.g., need to flag these nodes as “boundary
>>>    conditions” so they get handled properly during assembly of the
>>>    solution matrices, then assign velocities,…).
>>>
>>>    Here is the background for why I ask this question:
>>>
>>>    One of the projects we are starting to develop in Aspect in my group
>>>    is instantaneous models for a specific
>>>    subduction zones. The key issue with these models is that we need to
>>>    define a starting thermal structure
>>>    that is based on the observed geometry of the subducted plate (e.g.,
>>>    from seismicity). There are different
>>>    was to do this, and I’ve done several of them for previous models
>>>    completed using Citcom.
>>>
>>>    Based on that experience, and given the AMR capabilities of Aspect,
>>>    I think the best (most accurate and easiest) way to
>>>    define the starting thermal structure is to run model in which you
>>>    have defined the surface of the plate
>>>    INSIDE the model (going down into the mantle) and then define fixed
>>>    velocities associated with this surface.
>>>
>>>    Note it is not necessary for the elements to conform to this surface
>>>    (no distortion of the grid), we can use refinement of the grid to
>>>    get accurate enough for our purposes.
>>>
>>>    Once the velocity conditions inside the mesh are defined together
>>>    with the normal external boundary conditions and an initial
>>>    temperature structure for the plates at the actual top of the mesh,
>>>    then we would run this model forward in time to kinematically
>>>    “subduct” the plate. This will allow us to create a smooth 3D
>>>    starting temperature models for our instantaneous dynamically-driven
>>>    models that follows the observed shape of the slab.
>>>
>>>    In addition to using this capability for the purpose describe above,
>>>    this would allow Aspect to also run what is commonly referred to as
>>>    “mantle wedge thermal models”, in which the subducted plate and
>>>    overriding plates are really used as boundary conditions on the
>>>    flow/temperature in the mantle between them. These models are
>>>    commonly used to look at the detailed thermal structure and melting
>>>    in the mantle wedge.
>>>
>>>    Cheers,
>>>    Magali
>>>
>>>    --------------------------------------------------
>>>    Professor of Geophysics & UCD Chancellor Fellow
>>>    Earth & Planetary Sciences Dept., UC Davis
>>>    Davis, CA 95616
>>>    2129 Earth & Physical Sciences Bldg.
>>>    Office Phone: (530) 752-4169 <tel:%28530%29%20752-4169>
>>>    http://mygeologypage.ucdavis.edu/billen/
>>>    --------------------------------------------------
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
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>>
>>
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>
>
> --
> Timo Heister
> http://www.math.clemson.edu/~heister/
> _______________________________________________
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--------------------------------------------------
Professor of Geophysics & UCD Chancellor Fellow
Earth & Planetary Sciences Dept., UC Davis
Davis, CA 95616
2129 Earth & Physical Sciences Bldg.
Office Phone: (530) 752-4169
http://mygeologypage.ucdavis.edu/billen/
--------------------------------------------------

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