[CIG-CS] Variable viscosity Stokes solver

[Shijie Zhong]

Oops, I meant to send that email only to Walter. Now it was sent to cig-cs, 
perhaps more people would be interested in the problem. 

Shijie


Shijie Zhong, Professor 
Department of Physics
University of Colorado at Boulder
Boulder, CO 80309
Tel: 303-735-5095; Fax: 303-492-7935
Web: http://anquetil.colorado.edu/szhong

---- Original message ----
>Date: Mon, 11 Apr 2011 13:08:46 -0600 (MDT)
>From: cig-cs-bounces at geodynamics.org (on behalf of Shijie Zhong 
<shijie.zhong at Colorado.EDU>)
>Subject: Re: [CIG-CS] Variable viscosity Stokes solver  
>To: "Walter Landry" <walter at geodynamics.org>,cig-cs at geodynamics.org
>
>
>It would be interesting to benchmark the results with 10^n viscosity variations 
>across an element against analytical solutions for Stokes' flow. If you are 
>interested in the benchmarks, I would offer some help.
>
>Cheers,
>
>Shijie
>
>Shijie Zhong, Professor 
>Department of Physics
>University of Colorado at Boulder
>Boulder, CO 80309
>Tel: 303-735-5095; Fax: 303-492-7935
>Web: http://anquetil.colorado.edu/szhong
>
>---- Original message ----
>>Date: Mon, 11 Apr 2011 11:37:32 -0700 (PDT)
>>From: cig-cs-bounces at geodynamics.org (on behalf of Walter Landry 
><walter at geodynamics.org>)
>>Subject: Re: [CIG-CS] Variable viscosity Stokes solver  
>>To: cig-cs at geodynamics.org
>>
>>Moving this discussing to the cig-cs list.
>>
>>Wolfgang Bangerth <bangerth at math.tamu.edu> wrote:
>>> 
>>>> Taras Gerya manages to get up to 10^6 viscosity jumps for this problem
>>>> by using continuations.  However, when doing geophysical runs, he
>>>> never needs it.
>>>> 
>>>> Rhea has some large viscosity variations in their simulations, but I
>>>> do not think that their element-to-element variation is this large.
>>> 
>>> I don't think so either. In Rhea, the viscosity is determined by the 
>>> temperature and flow field, and a variation in eta so large would require an 
>>> element-to-element variation in temperature or strain rate that is also 
very 
>>> large. I do not believe that you would be able to get such variations in 
>>> solution fields of this magnitude from most reasonable finite element 
>methods 
>>> -- you need to stabilize methods to resolve variations this large, and this 
>>> tends to spread the variation out over several cells, which would then also 
>>> spread out the variation in viscosity. 
>>> 
>>> In other words, requiring a solver to be able to deal with such large 
>>> viscosity variations is not something you'd likely encounter in a code in 
>>> which the viscosity is not a parameter but a function of other variables.
>>
>>In problems with faulting, we can get arbitrarily small regions with
>>arbitrarily large viscosity jumps.  We can apply a limiter in order to
>>get a convergent algorithm, but the viscosity gradient will still be
>>very sharp.  For example, in Gale's dike example, the viscosity
>>variation is (I think) 10^5 element-to-element.  That is why I ended
>>up using a direct solver for it.
>>
>>>> Dave May's solver handles 10^6, but he aligns the boundary of the
>>>> falling box with the edges of the element.
>>> 
>>> That actually leads to another interesting question: if the interface is not 
>>> aligned, what do you use to integrate the local matrices and vectors? If 
your 
>>> coefficient, Gauss formula are no longer useful. Presumably an iterated 
>Gauss 
>>> formula, or something else of low order would be more appropriate.
>>
>>Gale partitions the element up with Voronoi cells centered around each
>>particle.  The viscosity is assumed smooth on those cells.  So the
>>integration is essentially done by using the particles as integration
>>points.
>>
>>I have also seen good results for other problems by using a higher
>>order field (e.g. fourth order) for material properties.  I do not
>>know if that will work for these problems.
>>
>>Cheers,
>>Walter Landry
>>walter at geodynamics.org
>>
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