[aspect-devel] How ASPECT overcomes numerical diffusion?

[Rene Gassmoeller]

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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