[aspect-devel] Flow through free surface

Scott King sdk at vt.edu
Tue Jan 30 03:45:10 PST 2018

```There are people out there who have worked on coupled erosion/convection problems.   I’m pretty sure Chris Beaumont and Sean Willis have papers from the mid-1990’s and perhaps Louis Moresi.    Here is one example I came across quickly.   You may know of this work, but I would look at how they have implemented erosion.

http://onlinelibrary.wiley.com/doi/10.1029/2001JB000433/abstract

> On Jan 29, 2018, at 11:49 PM, Lev Karatun <lev.karatun at gmail.com> wrote:
>
> If someone could give me an idea of whether what I'm thinking of is realistic or not, I'd appreciate it!
>
> Best regards,
> Lev Karatun.
>
> 2018-01-17 20:50 GMT-05:00 Lev Karatun <lev.karatun at gmail.com <mailto:lev.karatun at gmail.com>>:
> 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 <mailto: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 <mailto:bangerth at colostate.edu>
>                            www: http://www.math.colostate.edu/~bangerth/ <http://www.math.colostate.edu/~bangerth/>
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