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21h
comment Vortex in a Pipe / Solutions or approximations?
What is your objective here? If you just want to see a vortex move down a pipe, you can get by with potential flow probably. But if you want to look at vortex bubble breakdown, or heat transfer, or.... just about anything else, you'll need more. Can you explain what the objective of your study is and what you are hoping to learn?
2d
comment Liquid jet in the absence of gravity
What do you mean "Can we make liquid jets where there's no gravitational force?" Of course we can -- we take some liquid to space and make it shoot out through a hole. That's a liquid jet without gravity. Is there something more specific you're looking for?
2d
comment Interpretation of Eigenvalues and Eigenvectors of an hyperbolic conservation law $\partial_t W + A \partial_x W = 0$
@AmineHANINI It looks like you skipped a step -- you found the eigenvectors and eigenvalues of $\mathcal{A}$, not of $J^{-1} \mathcal{A} J$. In other words, you didn't symmetrize $\mathcal{A}$ first.
2d
comment Interpretation of Eigenvalues and Eigenvectors of an hyperbolic conservation law $\partial_t W + A \partial_x W = 0$
And it works in any dimension. But, in higher dimension you cannot (at least for the Euler equations) diagonalize both dimensions at the same time. Read through the linked PDF, it explains pretty well what happens and it provides all of the equations needed to work through and verify the answers for 1D and 2D in both conservative and non-conservative form of the Euler equations.
2d
comment Interpretation of Eigenvalues and Eigenvectors of an hyperbolic conservation law $\partial_t W + A \partial_x W = 0$
@AmineHANINI Doing things with non-linear equations throws it entirely out the window. What we do in the Euler equations is assume the Jacobian is fixed and this makes the equation "linear", or sometimes called quasi-linear. It's only true in a small neighborhood around a particular operating point, but that's enough to do the analysis needed. Regarding your question about the Shallow Water Equation -- I'm guessing that is the equation you need to do this for? I'll happily answer specific questions about particular steps, but I won't do the full derivation -- that is an exercise for you to do.
Feb
5
comment Interpretation of Eigenvalues and Eigenvectors of an hyperbolic conservation law $\partial_t W + A \partial_x W = 0$
The problem is A) identical copy-paste, B) no notice given that it was in both places, C) no attempt to tailor it to the specific audience, D) posted within 4 hours of each -- seemingly indicating that it was taking too long for an answer on Math so it was posted here. All of those things are against the norms we have here. I can't speak for Math.SE, they may be totally cool with it and that's why I just left a comment with a link to the cross-post, but SO as a whole doesn't like it, and we don't here either. There's no penalty because the question is a good one, but it does burn goodwill.
Feb
5
comment Interpretation of Eigenvalues and Eigenvectors of an hyperbolic conservation law $\partial_t W + A \partial_x W = 0$
Cf. meta.physics.stackexchange.com/questions/6963 meta.physics.stackexchange.com/questions/4133 meta.physics.stackexchange.com/questions/7413 meta.stackexchange.com/questions/64068 meta.physics.stackexchange.com/questions/6793 meta.physics.stackexchange.com/questions/888
Feb
5
comment Interpretation of Eigenvalues and Eigenvectors of an hyperbolic conservation law $\partial_t W + A \partial_x W = 0$
Sigh... this is cross posted at Math.SE. It's very poor form to cross-post identical questions on multiple sites.
Feb
5
revised Interpretation of Eigenvalues and Eigenvectors of an hyperbolic conservation law $\partial_t W + A \partial_x W = 0$
deleted 82 characters in body
Feb
5
answered Interpretation of Eigenvalues and Eigenvectors of an hyperbolic conservation law $\partial_t W + A \partial_x W = 0$
Feb
4
comment Why is the Pythagorean Theorem used for error calculation?
@Danu It is about experimental (or numerical) analysis, I'm inclined to leave it here because those things are on-topic here. Although I don't find it to be a particularly high-level question in those areas so I don't find it all that great of a question. But I think it's at least on-topic.
Feb
3
comment publication ethics
I'm voting to close this question as off-topic because it is not about physics; perhaps Academia.SE is a better fit.
Feb
2
comment Why is an airplane propeller so different from a boat propeller in shape?
Additional factors -- power required to spin fast enough to generate power and the effect of weight on getting into the air vs floating on the water.
Feb
2
comment Is flow speed between two pressures dependent on absolute or relative pressure difference?
@Chris Not initial flow speed, but acceleration. It boils down to $F = ma$ -- if your pressure is different because you crammed more mass into one side than the other, then it makes sense it will accelerate slower than if the pressure is increased because it is hotter (but density/mass is otherwise the same). We're only looking at initial acceleration here at the moment the fluid feels the gradient kick in.
Feb
1
comment Rotating fluid boundary layer
This is in any basic textbook for viscous flows. Either as an exercise for the reader or they give it as a derivation.
Feb
1
answered Is flow speed between two pressures dependent on absolute or relative pressure difference?
Jan
31
answered Simulating supersonic flight in game
Jan
31
comment Simulating supersonic flight in game
Also look up panel methods if you want some really fast approaches
Jan
31
comment Simulating supersonic flight in game
And for what it's worth, compressible flow is actually easier to solve than incompressible. Incompressible flow requires solving a Poisson equation while compressible is all hyperbolic and you can just march happily forward in time.
Jan
31
comment Simulating supersonic flight in game
Look up potential flow -- there are subsonic, trans-sonic and supersonic forms. For a game, there is no way you would need the full Navier-Stokes or Euler equations.