harmonic computation

[spinynormal]

hello bertholet,

i didn find anything about the discretizing for the harmonic field applying nonzeroflux boundries, i read mostly all papers wich are reffered, can i might ask for some hints! or did u discretize your self ?

best regards

[bertholet]

Hi spiny normal.

This was part of my master's thesis, feel free to check it out! I just added it to the git repo, it is called "DEC in a week". In the chapter about vector field design and about the fluid Simulation I also wrote about boundary constraints, you may also find further references in the thesis.

Hope this helps!

[spinynormal]

it does for sure! =) thanks for the response !

[spinynormal]

Hey peter, i would love to ask you one last time, in the paper from Stable, Circulation-Preserving, Simplicial Fluids, is a note and it says if there is a harmonic part the text is wrong, since the title is Computing the Harmonic Component on Flat Bordered Meshes and since harmonic 1-form doesnt exist on a sphere, the whole thing wouldn work out for a obstacle on a Sphere. right ? just to make sure ^^

[bertholet]

No, it would work out. There are no non-trivial one-forms on the sphere, but the constant zero is a harmonic one-form. So on the sphere it just gets simpler: no need to compute the harmonic part. But forces can still induce flow (...in the thesis there also are screenshots from a fluid sim on a sphere)

Out of interest - what are you trying to do? (-:

[spinynormal]

Hey peter thanks for responding again! =) if we have a sphere with a hole, vortex shedding would still appear ? when i read first time elcotts paper i assumed we are computing the harmonic flow of a vectorfield and also the harmonic component deals with singularities on a boundrynode like described in the vectorfield design chapitel in your thesis,

just trying to understand how to handle boundries on curved surfaces for viscous fluid , i am sorry for my non github related questions :/

[bertholet]

Vortex shedding is a "local" effect, when the fluid flows along an obstacle. This can potentially always take place, also on a sphere. On the other hand the existance of a harmonic form is a _topologica_l question and purely depends on the characteristic of the shape. The special thing on a sphere is that you cannot înduce a flow on its surface by specifying a harmonic vector field (as there is no non-trivial harmonic field there). But none-the -less you can apply (fixed or non fixed) forces to get the fluid flowing and hitting obstacles (that then can create vortices).

On a side note: by punching holes into the sphere you change its topology, and depending on the kind of constraint on added boundaries you can have harmonic fields. If the "holes" are just impenetrable boundaries there still is no harmonic component, but you have to add one additional zero vorticity constraint around each obstacle, if I remember correctly. You can also add a source and a sink on your sphere to induce some flow (or more sources and sinks), this will also "change the topology of the sphere" as far as the vector field is concerned, just as punching holes does (e.g. adding a source and a sink will make the sphere cylinder-like from a vector field / topological point of view and you can find a harmonic field...).

And no worries, ask anything you like (;

[spinynormal]

it makes intuitive sense, thanks peter!