0
$\begingroup$

I am reading the Fast Fluid Dynamics Simulation on the GPU article and stuck with the following part:

We can use the Helmholtz-Hodge Decomposition Theorem to define a projection operator, p.jpg , that projects a vector field w onto its divergence-free component, u. If we apply p.jpg to Equation 7, we get:

enter image description here

Could you please help me understand how we can derive this equation with the Helmholtz-Hodge Decomposition Theorem here and what is the physical interpretation in the context of this article this formula has?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

I don't have time to spell out the explanation in detail, but this idea is sketched out in the exercise 6.7 on page 228 of our book:

https://goldbart.gatech.edu/PostScript/MS_PG_book/bookmaster.pdf

Improve this answer
$\endgroup$
2
  • $\begingroup$ Thank you, but this is more a task to solve rather than the explanation. It brings to live other questions directed to use Helmholtz-Hodge Decomposition Theorem, but doesn't help me understand my case. I have even more information here: Helmholtz decomposition, but is still hard for me to catch how this leads to the formula above and especially what is the physical interpretation of this. $\endgroup$
    – Damir Tenishev
    Commented Sep 8, 2021 at 13:56
  • $\begingroup$ The basic idea is that the pressure does not dictate the motion of the fluid, but is instead a constraint which is dictated by the motion. The HH decomposition makes this clear. $\endgroup$
    – mike stone
    Commented Sep 8, 2021 at 16:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.