[CIG-MC] CitComCU bottom permeable boundary condition

[Bradford H. Hager]

Eh Tan-

I don't know if the slow convergence of the Stokes solver is related,  
but I do not think that the boundary condition that you describe is  
the one that Norm asked for and I do not think that it is physically  
meaningful.

I think that the proper boundary condition for a permeable top (or  
bottom) boundary condition, if no work is to be done on the boundary,  
is that the normal traction is a constant (e.g., zero).  That is, that

tau_rr = -p + visc*dVr/dr = constant.  (Since p is indeterminate to a  
constant, either the lithostatic p or 0 should work for the constant.)

The pressure, p. and dVr/dr do not need to be constant (or zero)  
individually,  just their sum (OK, their difference, since -p is  
involved.)

This boundary condition is easy to implement in ConMan - in fact, it  
can be viewed as the default - and has been used in many studies.  It  
should be easy to implement in the Cartesian version of CitCom.

But there is some complexity involved since Norm also asks that the  
flow be perpendicular to the boundary.  I now switch to Cartesian  
coordinates for simplicity, with x horizontal and z vertical.

At the bottom, Norm wants Vx = 0, so dVx/dx = 0 automatically.  But,  
if the material is incompressible, dVx/dx = 0 also means that dVz/dz  
= 0, so does not contribute to tau_zz (but specifying it explicitly  
is redundant and might lead to numerical problems.)  In that case,  
since dVz/dz must be zero to satisfy incompressible flow, the proper  
boundary condition is p = constant.

Brad Hager



On Apr 30, 2007, at 3:24 PM, Eh Tan wrote:

> Hi Norm,
>
> I don't know any implementation for permeable bottom boundary  
> condition
> available. I have tried to implement permeable top boundary condition
> before. Basically, the radial component of the velocity boundary
> condition becomes dVr/dr=0, instead of Vr=0. The implementation works,
> but it is extremely slow for the Stokes solver to converge. If you  
> need
> it, I can dig up the implementation for you.
>
>
> Cheers,
>
> -- 
> Eh Tan
> Staff Scientist
> Computational Infrastructure for Geodynamics
> 2750 E. Washington Blvd. Suite 210
> Pasadena, CA 91107
> (626) 395-1693
> http://www.geodynamics.org
>
>
>
>
> Norm Sleep wrote:
>> Has anyone implemented a permeable bottom boundary condition for any
>> of the CitCom codes? I know how to do this in 2-D stream function but
>> I have not tried it in 3-D?  That is,fluid exits the domain
>> perpendicular to the boundary, comes in at a given temperature, and
>> the boundary does no work on the domain of calculations.
>>
>> If not, is there another public source code that does this?
>>
>> Moore, W. B., G. Schubert, and P. Tackley (1998) Three-dimensional
>> simulations of plume-lithosphere interaction at the Hawaiian swell,/
>> Science/,/ 279/, 1008-1011.
>>
>> thank you
>>
>> Norm Sleep
>> --------------------------------------------------------------------- 
>> ---
>>
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>
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