[aspect-devel] Mass balance

[John Naliboff]

Hi Mohamed,

The code will always conserve mass according to the prescribed boundary conditions .. the question is whether your boundary conditions are balancing the influx/outflux.  

If done carefully, you can for all intensive purposes match the influx/outflux with prescribed boundary velocities … a good diagnostic for this is whether your average free surface elevation is changing with time.

I’ve attached a script where I computed boundary velocities for an extension problem using a different code.  Run the script with the command “python boundaryflux.py” from the terminal.  You will need python and numpy installed.

Let me know if you have any questions about what the code is doing, although it should be fairly clear from the comments.

Cheers,
John

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





> On Jun 21, 2016, at 12:20 AM, Mohamed Gouiza <M.Gouiza at leeds.ac.uk> wrote:
> 
>> -- 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.
> 
> Wolfgang: This is what I am doing now, but later I am going to extend my model to the lower mantle (y>650km) and I want to try mass conversation by introducing only lower mantle material, only upper mantle material, and both to see how does that impact the model.
> 
>> 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.
> I>f you would like, I can send the formula I used.
> 
> John: That should work too, although it wouldn't ensure total mass conservation. I would appreciate if you can send me the formula. 
> 
> If I use the Box with lithosphere boundary indicators, and use zero traction boundary for the left and the right (in addition to the bottom), and prescribed velocity for left lithosphere and right lithosphere, would that work?
> 
> Cheers,
> Mohamed
> 
> -----Original Message-----
> From: Aspect-devel [mailto:aspect-devel-bounces at geodynamics.org] On Behalf Of Wolfgang Bangerth
> Sent: 21 June 2016 07:27
> To: aspect-devel at geodynamics.org
> Subject: Re: [aspect-devel] Mass balance
> 
> 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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