[aspect-devel] How ASPECT overcomes numerical diffusion?

[Magali Billen]

I'll add to Rene's comment about composition advection with fields. Ying He as recently contributed a Bound Preserving limiter to the discontinuous galerkin method for composition advection in Aspect.  This allows sharper boundaries to be maintained compared to the FEM on the same mesh size. Ying is still working on improving the performance of the algorithm in Aspect.  I've attached some example figures from a paper Ying has just finished and is submitting for publication this week.  If
anyone wants more details let me know and we can forward a preprint.

I don't know if this is included in the new release or not  - I've cc'd Ying to provide more information (I think there is a pending pull request). 

For model with viscosity contrast between box and surroundings of 10:1  (zoom in on pics to see mesh and details of boundary)
Deformed box is after 5000 time-steps.

Viscosity contrast of 1:1  (eta(C), C = 0 or 1)

From one of the Aspect cookbooks (left is DG-BP and Right is FEM in Aspect):


On May 18, 2016, at 9:19 AM, Rene Gassmoeller <r.gassmoeller at mailbox.org> wrote:

> Hello Qingwen,
> it is true that interfaces between compositional fields diffuse during advection, and this is a well known problem in fluid dynamics in general. However, the amount of diffusion is dependent on the resolution of the model and with higher resolution the amount of artificial diffusion converges towards zero with the size of the cell, so in practice the code is not 'wrong' it maybe just needs a higher resolution for your problem. 
> It is also true that particle based methods do not suffer from this particular problem since values on one particle can stay constant over time (and an interface appears sharp even at the end of the model). Nevertheless, particle methods suffer from other numerical artifacts like the interpolation between particle positions and mesh positions and introduce an additional advection error by integrating the particle positions over time. That being said particle methods have the same property to converge towards the correct solution with increasing resolution and number of particles, so they are not 'wrong' either. It just depends on the type of problem you want to solve, if grid-based methods or particle methods are more effective. The problem can likely be solved by both.
> 
> Hope that helps your understanding of the problem,
> Best,
> Rene
> 
> 
> On 05/18/2016 10:43 AM, ZhangQingwen wrote:
>> Hi all,
>> I have been curious that, if several composition fields advect passively with a given velocity field, the boundaries between these composition fields will not be as sharp as they were, or more seriously, the code goes wrong, so how dose ASPECT deal with this issue of numerical diffusion? 
>> For some particle-based (or, marker-based) codes like Underworld, it is not a problem because advection relies on extra passive particles moving with velocity field and artificial errors will be minimized.
>> 
>> Best,
>> Qw
>> 
>> 
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