2:31 AM
@KyleKanos Is there a standard way or program to give a triangulation of the dicretization of space? How can you specify the region with more points? I don't really understand this so I never try to use FVM

Usually FVM uses rectangular grids

What is the point of using FVM then?

Ease of programming + Adaptive Mesh Refinement

Do you mean that you can change the grid size during simulation?

Yes

2:34 AM
I have to use small grid size sometimes during runtime because the method is not accurate, but I have not use FVM
So, what is the difference?
I use two difference grid size and compare and determine whether I want to use a small one.

AMR kicks in when the difference between adjacent cells is above a certain value
The grids around that jump are cut in half (in a new struct)
The new solutions with the smaller grids are then later merged with the larger grid

Usually, I resize the lattice size by a factor of 2 for all lattice for easy implementation. So, you mean FVM can resize only a local region?
BTW, what is AMR?

No, FVM doesn't do anything like that. It's the AMR that does it
It's a separate thing from the FVM

So, can AMR adapt only a local region?

Yes
The idea is that you don't want to run a 5000x5000 simulation because it will just waste computing time in the regions where nothing is really happening

2:41 AM
I know the core idea of FVM, but I don't know how the AMR really work out
DO you have a reference or link to a real example that I can follow?

So if you instead run a 50x50 base with say 7 levels of refinement, then you get 50^2 * 2^7 = 6,400 x 6400 resolution

@KyleKanos Ya, change dx also require dt to change, so the total simulation time is even worse

@hwlau Nope, it's better
The resolution is only high in regions of interest and very low everywhere else
Suppose your domain is from 0 to 10

@KyleKanos Are you talking about the FVM?

@hwlau No, the AMR makes the run time faster than without it at high resolution

2:46 AM
@KyleKanos Is it still stable?

Of course!
But any way...if your simulation is really strong in the range 0 to 2
Then your resolution would be very high in that range and at the coarsest level everywhere else

@KyleKanos > DO you have a reference or link to a real example that I can follow?

I'm trying to find a really good one

Is the AMR criteria universal for different nonlinear differential equation?
And how can I choose the error estimator?

3:13 AM
The 2d and 3d implementation is complicated
it is easy to messy thing up
BTW, there is no good answer on it on scicomp.SE

5 hours later…

@KyleKanos: I guess you know about "fluids" very well...
(as @tpg isn't here) :D

8:04 AM
On the other day, I saw tpg's "nozzle" answer, where he mentioned something about supersonic flows
Got it...
> When we look at subsonic flow, the gas speeds up as the area decreases and slows down as the area increases. This is the traditional Venturi effect. However, when the flow is supersonic, the opposite happens. The flow accelerates as the area increases and slows as it decreases.
^^^ This thing gets me...
I'm unable to comprehend that :/

8:24 AM
To @Brandon Enright (and other editors): I would suggest to use the tag as little as possible, as explained in its tag wiki.

2 hours later…
user54412
10:02 AM
@Waffle'sCrazyPeanut Maybe this will help: nakka-rocketry.net/th_nozz.html

user54412
well, it doesn't offer any good intuition, but it derives the appropriate equations (they're not too complicated)

10:59 AM
@hwlau AFAIK, AMR should be useful for any partial differential equation. Usually one of the fluid variables (density or pressure really) are chosen as the error check with discrepancies larger than say 0.02 between the two cells flagging it for refinement.
I've never actually programmed an AMR engine in any dimension, just taken what other people have done. I have done a SMR (Statis Mesh Refinement) which is where only a certain region is refined and the solution is smoothed onto the coarse solution.
I've been thinking of throwing that one up on github, but I've been lazy
@hwlau Yes, no answers on SciComp because most of the answerers use the FEM method

5 hours later…
4:18 PM
Do you guys think that the question: "Can we measure the rotation of the Earth around the Sun from inside a laboratory?" would be on-topic?

user54412
5:16 PM
@jinawee why not?

5:48 PM
The Riemannium atom? Is it possibly real or does it not abide to certain conditions for existence?

user54412
6:21 PM
@dmckee If I see a user profile that says "Please delete me" should I inform the mods? (maybe the user forgot to notify someone through the proper channels)

@jinawee Sure, but the answer is going to be massively complicated by competition from the rotation of the planet. Maybe a really big Foucault pendulum at the rotational pole, but protecting it against noise and backgrounds for months is not going to be easy.
@ChrisWhite According to physics.stackexchange.com/help/deleting-account they are suppose to also use the contact link to bring it to the attention of the team. We can't kill most accounts.
On the pendulum...would the equator be better. One involves subtracting of the daily rotation.

user54412
@dmckee ok, so it's a team thing, not a mod thing

user54412
it's weird, I found an account like this, but the user posted a question a few minutes ago

user54412
@GlenTheUdderboat you're going to have to define Riemannium - I've never heard of it

Hey all
Anyone Interested in QCQI

2 hours later…
8:24 PM
0

Simple as that. I think that since we can only upvote comments, it leads to skew, where comments, even if they are unhelpful or inaccurate cannot be downvoted. Given that the whole mechanics of this website is, more-or-less "people vote for things and the good things rise to the top, while the ...

8:42 PM
@ChrisWhite yeah, I think we know about one case. Anyway, it never hurts to bring it to moderators' attention, but it's not really something we can deal with.

9:01 PM
1

We've previously had some discussion about the suitability of pure math questions for this site. Currently, pure math questions - by which I mean those that have no physics content, even if they arise in a physical context - are off topic. We migrate those to Mathematics. Here are some recent exa...

9:15 PM
@KyleKanos I know now that why people usually use finite different because it can be easily written from scratch. In particular when you get new differential equations. The AMR is hard to implement and it costs months to make it correct.

@hwlau FDM is trivial because it's simple differences of adjacent cells

@KyleKanos Are you using some kind of public library or in-house one?

FVM requires smoothing of the data (interpolation) for more accuracy

@KyleKanos yup, but the PDE can't be very non-trivial. You will certainty want to gurantee it is correct before you do anything else

I am using a modification of a public library (full disclosure: I didn't do a drop of work on the AMR engine, that was all done by other people)
The code bases the AMR on Chombo

9:17 PM
@KyleKanos Is the smoothing gurantee some kind of conservation of mass/energy/probabilty?

@hwlau No, it improves the accuracy of the computation.

What is the point if the mass disappear after some time of simulation?
I just find that I confused with the FVM and FEM somehow

Unless you have free boundaries, mass won't just disappear

@KyleKanos You know the FDM of diffusion equation (or similar) has stability criteria, how can it be solved in AMR
In particular, can I use implicit method in AMR?

I don't think it would change any
The AMR engine still detects if there is a discrepancy and adds new structs as necessary
Your code would call the solver regardless

9:29 PM
The criteria is something like dx/dt^2, how can it adapt a different time step to satisfy the stability criteria

The criterion is 0.5 <= k*dt/dx/dx

sor, yes
but if you use small dx, would you change dt?

It depends
Some AMR engines would change it and others would not

So, do you mean that I only need to give the relation between different nearest neighbour gird point, and the AMR engines will calculate other things for me? Is it the reason you think that the method can be used for all partial differential equation?

2 hours later…
11:32 PM
@dimension10 I noticed you have a "fake" Sklivvz over at PO. Can you please delete the user and only leave the attribution on posts/comments (unless you want to remove them as well, but that's up to you).
@dilaton ^