If anyone's wondering about the motivation behind curl and divergence:
Most interesting fluids (i.e. water) are incompressible, which means that their divergence is always 0 (see slide 22). This helps simplify the mathematics, allowing the faster solver presented in the following slides.
Because the divergence is 0, Green's theorem is also applicable, although I don't think that's discussed here.
modatberkeley
@sberkun Is divergence necessarily 0? (when we account for a non-zero net in/out flow of region)
modatberkeley
I misread sberkun's comment. I now understand why divergence is 0 after looking at slide 22 on non-compressibility of fluids.
ShrihanSolo
This is my favorite video to understand divergence and curl better: https://www.youtube.com/watch?v=rB83DpBJQsE&vl=en&ab_channel=3Blue1Brown
If anyone's wondering about the motivation behind curl and divergence:
Most interesting fluids (i.e. water) are incompressible, which means that their divergence is always 0 (see slide 22). This helps simplify the mathematics, allowing the faster solver presented in the following slides.
Because the divergence is 0, Green's theorem is also applicable, although I don't think that's discussed here.
@sberkun Is divergence necessarily 0? (when we account for a non-zero net in/out flow of region)
I misread sberkun's comment. I now understand why divergence is 0 after looking at slide 22 on non-compressibility of fluids.
This is my favorite video to understand divergence and curl better: https://www.youtube.com/watch?v=rB83DpBJQsE&vl=en&ab_channel=3Blue1Brown