[CIG-LONG] CIG-LONG Digest, Vol 51, Issue 2 Alleviating pressure singularity in corner-flow mantle-wedge subduction zone model
mspieg
mspieg at ldeo.columbia.edu
Tue Feb 15 09:11:49 PST 2011
Hi Karen,
in general, with those boundary conditions (and an iso-viscous
model) the pressure will be singular in the corner and essentially
unresolvable. However, a useful trick for regularizing the
singularity is to smooth out the top velocity a bit e.g. setting the
horizontal velocity on the top to something like vx=erf(x/\lambda)
(alternatively tanh(x/lambda)) vy=0 where lambda is some length-
scale of your choice (and approaches corner flow in the limit \lambda-
> zero). In this case, you can't set the lhs boundary to have
dirichlet boundary conditions but it's okay to set it up as a
reflection boundary with vx=0 and reflection/Natural Neumann
conditions dvy/dx = 0 (essentially zero shear stress). We do
this for magma problems at ridges all the time as the singularity is
actually unphysical (but demanded from an isoviscous corner flow
solution).
Not entirely sure how to implement that in GALE but I'm sure Walter
can help.
Hope that's useful
cheers
marc
On Feb 15, 2011, at 11:57 AM, Karen Paczkowski wrote:
> Hi Walter,
>
> Thank you for the advice and input file. I am having trouble using
> the gradient region to alleviate the negative pressure singularity
> with velocities that diverge from the corner.
>
> Specifically, if the left side has a velocity of vy = -1 and vx = 0
> and then the top is either fixed with vx=vy=0 or extending vx = 1
> and vy = 0 a source like flow forms radiating out of the corner.
> Since no material is allowed into the corner, due to the fixed
> velocities in the triangular corner shape, a huge negative pressure
> singularity develops. It grows from ~300 with no triangular
> gradient region to ~ 800 with vx=vy=0 and 1400 with vx = 1 and vy =0.
>
> I have attached my input file. It is currently in the configuration:
>
> Left: vx =0 and vy = -1
> Top vx = 1 and vy = 0
>
> Thank you,
> Karen
>
>
> <CornerFlowWithGradient_vx1Top.xml>
>
> Pressure and Velocity Field with no fixed corner region:
>
>
> <NoGradientCorner.png>
>
> Pressure and Velocity Field with a fixed corner region:
>
> <GradientCorner.png>
>
>
> On Feb 12, 2011, at 2:48 PM, cig-long-request at geodynamics.org wrote:
>
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>> Today's Topics:
>>
>> 1. Alleviating pressure singularity in corner-flow mantle-wedge
>> subduction zone model (Karen Paczkowski)
>> 2. Re: Alleviating pressure singularity in corner-flow
>> mantle-wedge subduction zone model (Bradford H. Hager)
>> 3. Re: Alleviating pressure singularity in corner-flow
>> mantle-wedge subduction zone model (Walter Landry)
>>
>>
>> ---------------------------------------------------------------------
>> -
>>
>> Message: 1
>> Date: Fri, 11 Feb 2011 15:06:36 -0500
>> From: Karen Paczkowski <karen.paczkowski at yale.edu>
>> Subject: [CIG-LONG] Alleviating pressure singularity in corner-flow
>> mantle-wedge subduction zone model
>> To: cig-long at geodynamics.org
>> Message-ID: <8278D009-9828-40B1-B7C4-90C534D5965A at yale.edu>
>> Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes
>>
>> Hi,
>>
>> I am trying to write a simple corner-flow mantle-wedge subduction
>> zone
>> model using Gale. Since, in the corner of the wedge the velocity
>> abruptly changes from v=vslab along the slab to v=0 along the
>> overriding plate a pressure singularity develops in the corner of the
>> wedge.
>>
>> I was wondering if anyone else has encountered this issue and what
>> they did to alleviate the pressure singularity in the corner?
>>
>> I have tried adding a small shape along the slab-mantle interface
>> right near the corner that has a velocity with a gradient going from
>> v=0 to v=slab over a couple of resolution points. This mainly seems
>> to move my pressure singularity around, but not elimiate it.
>>
>> Any advice people have on alleviating the pressure singularity in a
>> corner-flow subduction model would be greatly appreciated.
>>
>> Thank you,
>> Karen
>>
>>
>>
>>
>>
>> ------------------------------
>>
>> Message: 2
>> Date: Fri, 11 Feb 2011 18:02:54 -0500
>> From: "Bradford H. Hager" <bhhager at MIT.EDU>
>> Subject: Re: [CIG-LONG] Alleviating pressure singularity in
>> corner-flow mantle-wedge subduction zone model
>> To: Karen Paczkowski <karen.paczkowski at yale.edu>
>> Cc: CIG <cig-long at geodynamics.org>
>> Message-ID: <5A320C85-2D13-44B7-9F5E-702C3679C2CE at mit.edu>
>> Content-Type: text/plain; charset=us-ascii
>>
>> Instead of imposing a velocity gradient, try allowing a few nodes
>> to be free - that way they can determine the appropriate velocity
>> gradient.
>>
>> Brad Hager
>>
>> On Feb 11, 2011, at 3:06 PM, Karen Paczkowski wrote:
>>
>>> Hi,
>>>
>>> I am trying to write a simple corner-flow mantle-wedge subduction
>>> zone
>>> model using Gale. Since, in the corner of the wedge the velocity
>>> abruptly changes from v=vslab along the slab to v=0 along the
>>> overriding plate a pressure singularity develops in the corner of
>>> the
>>> wedge.
>>>
>>> I was wondering if anyone else has encountered this issue and what
>>> they did to alleviate the pressure singularity in the corner?
>>>
>>> I have tried adding a small shape along the slab-mantle interface
>>> right near the corner that has a velocity with a gradient going from
>>> v=0 to v=slab over a couple of resolution points. This mainly seems
>>> to move my pressure singularity around, but not elimiate it.
>>>
>>> Any advice people have on alleviating the pressure singularity in a
>>> corner-flow subduction model would be greatly appreciated.
>>>
>>> Thank you,
>>> Karen
>>>
>>>
>>>
>>> _______________________________________________
>>> CIG-LONG mailing list
>>> CIG-LONG at geodynamics.org
>>> http://geodynamics.org/cgi-bin/mailman/listinfo/cig-long
>>
>>
>>
>> ------------------------------
>>
>> Message: 3
>> Date: Sat, 12 Feb 2011 11:47:44 -0800 (PST)
>> From: Walter Landry <walter at geodynamics.org>
>> Subject: Re: [CIG-LONG] Alleviating pressure singularity in
>> corner-flow mantle-wedge subduction zone model
>> To: karen.paczkowski at yale.edu
>> Cc: cig-long at geodynamics.org
>> Message-ID:
>> <20110212.114744.1837452039028910477.walter at geodynamics.org>
>> Content-Type: text/plain; charset="us-ascii"
>>
>> Karen Paczkowski <karen.paczkowski at yale.edu> wrote:
>>> Hi,
>>>
>>> I am trying to write a simple corner-flow mantle-wedge subduction
>>> zone
>>> model using Gale. Since, in the corner of the wedge the velocity
>>> abruptly changes from v=vslab along the slab to v=0 along the
>>> overriding plate a pressure singularity develops in the corner of
>>> the
>>> wedge.
>>>
>>> I was wondering if anyone else has encountered this issue and what
>>> they did to alleviate the pressure singularity in the corner?
>>>
>>> I have tried adding a small shape along the slab-mantle interface
>>> right near the corner that has a velocity with a gradient going from
>>> v=0 to v=slab over a couple of resolution points. This mainly seems
>>> to move my pressure singularity around, but not elimiate it.
>>>
>>> Any advice people have on alleviating the pressure singularity in a
>>> corner-flow subduction model would be greatly appreciated.
>>
>> Have you tried fixing the velocity within the box near the corner?
>> Specifically, you can try using a MeshShapeVC on a region near the
>> corner.
>> This should remove the pressure singularity, because you are no
>> longer
>> solving near the singular point.
>>
>> To illustrate, I am attaching two input files. There are still some
>> issues at the edge of the MeshShapeVC because the matching is not
>> exact, but the error is much smaller. Without the fix, the pressure
>> goes up to 213. With the fix, the max pressure is about 7.
>>
>> Cheers,
>> Walter Landry
>> walter at geodynamics.org
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>> ------------------------------
>>
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>> End of CIG-LONG Digest, Vol 51, Issue 2
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>
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----------------------------------------------------
Marc Spiegelman
Lamont-Doherty Earth Observatory
Dept. of Applied Physics/Applied Math
Columbia University
http://www.ldeo.columbia.edu/~mspieg
tel: 845 704 2323 (SkypeIn)
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