P31

Air and Smoke

✅ 前面讲的是怎么更新速度；后面讲怎么利用速度做出效果。

  • To simulate air and water, we need to advect some physical quantities.
    • Smoke (density); water (volume-of-fluid, or signed distance function)
    • Volume loss issue in water (how to fix it?)
    • If you need to create a mesh from grid for rendering, you need something like marching cube.

P32

Air Simulation

  • Air simulation is done in two steps.
  • In Step 1, we update the flow (the velocity field) \(\mathbf{u}\).
  • In Step 2, we use semi-Lagrangian (page 22) advect all of the other physical quantities, i.e., density, temperature…
  • Typically we use Dirichlet boundaries for an open space (or Neumann boundaries for a container.)
  • We can use it to simulate underwater as well.

P33

Water Simulation

✅ 要渲染的不是水，而是水与空气的接触面。但通常只模拟水不模拟空气。

  • Two representations

    • Volume-of-fluid (as the name suggests…)

    ✅ 表示1：例如一个格子存储水的体积的百分化。用于早期，无法描述水的界面，因此不精准。

    • A signed distance function defined over the grid.

    ❓ 怎么计算一个格子中的水的百分比？

  • How to advect(更新)?

    • Semi-Lagrangian (volume loss)
    • Level set method (volume loss)，专用于 SDF 表示方法

    ✅ 水变少是常见问题，两种advect都存在。

P35

After-Class Reading

Osher and Fedkiw.
Level Set Methods and Dynamic Implicit Surfaces.

✅ 介绍流体模拟的很好的书。

本文出自CaterpillarStudyGroup，转载请注明出处。

https://caterpillarstudygroup.github.io/GAMES103_mdbook/