Stable Fluids - Idea
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- \(\displaystyle \frac{\partial u}{\partial t}=f-(u\cdot \nabla) u+\nu\triangle u -\frac{1}{\rho}\nabla \mathrm{p}\)
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- - \(1/\rho\;\nabla \mathrm{p}\): Pressure term only used to ensure divergence free
- - Similar to Lagrange multipler for constraints
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- Remove pressure term
- Replace by explicit projection on divergence free vector field \(\mathrm{P}\)
- \(\displaystyle \Rightarrow \frac{\partial u}{\partial t}=\mathrm{P}(f-(u\cdot \nabla) u+\nu\triangle u)\)
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- Compute each terms one after the other
- \(u^{k} \underbrace{\to}_{ \small{add forces} \atop f} u_1^k \underbrace{\to}_{\small diffuse \atop \nu \triangle u} u_2^k
\underbrace{\to}_{\small project \atop \mathrm{P}} u_3^k \underbrace{\to}_{\small advect \atop (u \cdot \nabla) u } u^{k+1}\)
