Question about evolving mesh

[TUZETF]

Hi, I am thinking of using VoronoiFVM.jl for solving a set of different PDEs governing the evolution of snow on the ground in 1D. In order to follow the ice-matrix in snow, it is usual to solve diffusion processes and water liquid percolation on a fix grid and then to update the grid (by moving nodes as snow settles) and iterate again on the new grid and so on.
I would like to know if according to you, VoronoiFVM could be applied in such a configuration.

Thank you by advance!

[j-fu]

Hi, I appreciate your interest in the code!.

I did not try such a problem yet, but I think that it is possible. It seems that the authors of https://doi.org/10.1016/j.compchemeng.2021.107412 were sucessful doing something like this.

Just a hint: wenn you just move the points (without adding or removing points), you can try to use the
update_grid! method to recalculate the control volume data, in order to avoid the creation of a new system.

Another interesting option would be the approach used in https://doi.org/10.1016/j.jcp.2012.06.005 , however I did not think yet about how to realize that in this package.

[TUZETF]

Hi!
Thank you very much for your quick response! I had a look to the articles you sent and I think that your package could fit out interest. We are at the start of the project for now and I am pretty new to the world of PDEs so I am not sure that I will use it at the end but if I do I will let you know (and cite your contribution of course).

I have an additional (probably stupid) question:
As far as I understand, you define the functions (e.g storage!) by broadcasting f to u (which appears to be of type Dual).
For now I do not fully understand what is behind but I would like to know how to define a spatially varying coefficient in one of these functions. For instance defining a diffusion coefficient that depends on your gridpoint.
I think that should be pretty easy to do but I don't find an example of that and prefer not digging in the code as I explore many different options at the same time.

[j-fu]

Ok, this is no really well documented:
https://j-fu.github.io/VoronoiFVM.jl/stable/physics/#VoronoiFVM.AbstractEdge
You should be able to do something like:

function flux( y, u, edge)
    x=0.5*(edge[1,1]+edge[1,2])
    y[1]=D(x)*(u[1,1]-u[1,2])
end

The dual number stuff allows to obtain the derivatives, e.g. in the case your D depends on u.