[aspect-devel] Mass balance

[John Naliboff]

Hi Mohamed,

The no-stress boundary is a good option.  

This is similar in nature to the ‘winkler’ boundary conditions that is frequently used.  See Popov and Sobolev 2008 (PEPI, vol 171) for a formal definition of the winkler boundary.  I am going to try and put this in as a boundary condition option soon.

If you want to use prescribed velocities only to ensure mass conservation, you can write out an equation where the horizontal velocity on the side wall varies by some function and sums to zero.  

For example, in the past I’ve had outflow down to 120 km, a transition from outward to inward velocity between 120 and 180 km, fixed inflow down to 240 km and inflow at the model base.  It is a just a matter of calculating the flux (integrating velocity over length of boundary) over different sections and setting velocities accordingly.  You can also combine the sidewall inflow/outflow with inflow at the model base.
If you would like, I can send the formula I used.  

Cheers,
John

*************************************************
Assistant Project Scientist, CIG
Earth & Planetary Sciences Dept., UC Davis


> On Jun 20, 2016, at 11:26 PM, Wolfgang Bangerth <bangerth at tamu.edu> wrote:
> 
> On 06/21/2016 01:20 AM, Mohamed Gouiza wrote:
>> 
>> 
>> I am runing a 2d model (box with x=500km; y=600km) with prescribed velocity
>> (ve) on left and right boundaries (if y>=120km & x<250km, Ve=-1cm/year, if
>> y>=120km & x>=250km, Ve=1cm/year).
>> 
>> So I am loosing lithospheric material with time and I would like to replace it
>> by astenospheric matrial. This is usually achieved by imposing a prescribed
>> velocity (Vm) to the sublithospheric mantle bounderies (opposite to the one
>> imposed to the lithospheric boundaries) to achieve masse balance with time. I
>> can run Several simulations and try to find an empirical relationship between
>> Ve and Vm, but I want to know if this can be done in more clever way?!
> 
> Mohamed -- why don't you just use no-stress boundary conditions at the bottom? This way, material will simply flow through the bottom as necessary to ensure mass conservation.
> 
> Best
> WB
> 
> -- 
> ------------------------------------------------------------------------
> Wolfgang Bangerth               email:            bangerth at math.tamu.edu
>                                www: http://www.math.tamu.edu/~bangerth/
> 
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