# [aspect-devel] Flow through free surface

Lev Karatun lev.karatun at gmail.com
Wed Jan 17 17:50:54 PST 2018

```Hi Wolfgang,

* You want the boundary to be free and move according to whatever flow you
> get below
>
My understanding is that this is the current implementation of free
surface?

For any more complicated procedure, it would be useful to first define
> exactly what equations you want to solve, and then (and *only* then) think
> about how you want to solve them.
>
What I was thinking of doing is either something as simple as eroding all
material that is above a specified elevation (in which case I don't even
need to solve a system of equations -- correct me if I'm wrong please), or
solving a diffusion equation (which (I think) I know how to solve).

Essentially, right now I know how to adjust the velocity of the surface
vertices according to the solution of the diffusion equation. But I don't
know how to superimpose the new boundary on top of the advected material.
Is it a realistic thing to do? How would I go about it?

Best regards,
Lev Karatun.

2018-01-17 16:03 GMT-05:00 Wolfgang Bangerth <bangerth at colostate.edu>:

> On 01/16/2018 01:53 PM, Lev Karatun wrote:
>
>>
>> I was wondering if you could give me an idea of how hard it would be to
>> allow material flow through the free surface? Right now I'm just able to
>> dampen the elevation change by applying the diffusion equation, but is it
>> possible to actually take material out of the system? Would the hardest
>> part be figuring out if a point is inside a curved domain? Or is there an
>> inherent limitation in Aspect that makes it not feasible in principle?
>> To rephrase what I mean: is it possible to let the material move at the
>> surface with Stokes velocity, and then draw the new top boundary on top of
>> it, getting rid of material that  was eroded away (falls outside of the new
>> model boundaries), and filling in the now less deep trenches with crustal
>> material?
>>
>
> Mathematically, the free boundary is of course determined just so that no
> flux goes across it.
>
> I think what you want is essentially a two-step process:
> * You want the boundary to be free and move according to whatever flow you
> get below
> * Then you want to erode away or deposit material on top of it.
>
> The easiest way to implement may be exactly to do this: do one; then do
> the other. For any more complicated procedure, it would be useful to first
> define exactly what equations you want to solve, and then (and *only* then)
> think about how you want to solve them.
>
> Best
>  W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth          email:                 bangerth at colostate.edu
>                            www: http://www.math.colostate.edu/~bangerth/
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