Lecture 17

Intro to fluids.

Thoughts

  • At the time I didn’t quite understand why the advection term of Navier-Stokes is u dot grad u, but the rest of it made a lot of sense. The idea is that the velocity field gets transported along itself (advected), so it follow for a component the derivative to ‘pull’ in the direction of the gradient of u, along u itself. This would make ‘accelerations’ within the fluid slow or speedup velocities depending on their alignment.
  • The Eulerian discretization resulted in some very compact code in Stam’s original paper, and seemed quite easy to implement. However, it seemed like the grid size needed to be quite small (hence taking up a lot of memory and computation) to get good results.
  • Stable fluids was surprisingly robust, I can see how it is still useful for simple/fast simulations today.
  • Talked a bit about particle based methods: SPH seems more natural to me than Eulerian methods, since fluids really are made up of tons of particles interacting within neighborhoods. Methods for collecting forces and surface meshing reminded me a lot of metaballs/marching cubes, etc.
Written on March 31, 2021