and it's a linear system so it's just a superposition of sine waves anyway

ye

which is all that matters

yeah

unless you care for some meme space of functions like L^1_loc or some obscure sobolev space

I don't even know what those are and frankly I'm probably better off for it lol

I probably got more out of FEM for understanding those than I did studying a bit of functional analysis

still fascinating stuff, nonetheless

oh this is probably a good opportunity for me to ask how FEM works

I feel I understand FVM pretty well and have even implemented my own custom FVM scheme that works really nicely, but I cannot understand how FEM is supposed to work

probably not, cause I only have a glimpse of it my friend

ah, damn

in some sense, you enforce global conservation instead of local conservation

instead of solving your equation "for every cell", you solve your equation "for every suitable test function" in a version that is called the "weak" or variational form of the equation

you integrate both sides and take products with those functions, enforcing that the equation is solved for every one of those in a suitable space of your choice

the hard part is generally converting your equation to weak form, especially when it is nonlinear, because you turn your differential into some kind of bilinear form, sometimes not even that

huh

yeah this reminds me of when I was researching it on the internet

all these concepts I have zero familiarity with

the formulation of FVM is not exactly simple either I was used to naive FDM and enforcing boundary conditions with FVM still gives me some trouble to derive

FVM, at least from an informal perspective, is pretty intuitive and straightforward. It's just the rigorous theory that gets pretty hairy, but I've been able to find good success without being thoroughly rigorous. As for boundary conditions, yeah those can be a little bit tricky in general since they have to respond appropriately according to the dynamics of the PDE being simulated, but again I've been able to manage decently on that front, if not perfectly, although idk if perfect boundary conditions even exist

One goal I haven't been able to achieve with FVM is inviscid behavior on very small scales, sustaining vorticity features maybe only 3 or 4 cells wide without diffusion. I've been able to achieve this with LBM and I've gotten FVM close but not all the way there. Note that everything I've done is for 2D flows only.

Is there an openFoam tutorial where they use komega sst for supersonic case?

grep in the tutorials folder 🙂 that is what I do

is openfoam wiki also down for others or just me?

same for me

Yeah it's been down for a couple of days along with the dl website

I encountered this earlier that day

I've been wanting to download it again on my new server but since the dl website is down I really only have two options: Build from source, or find an archive on something like archive.org and softwareheritage

Both of which I don't really have the time to mess around with until the weekend rolls around again 😔