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Lecture 4-06 fluid sim

Lecture 4-06 fluid sim - Fluids Lagrangian Eulerian...

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Fluids: Lagrangian, Eulerian techniques (13) file:///C:/stuff/content/misc/CS520/lectures/notes/lect_fluids/LagEuler.html#(1) 1 of 16 5/3/2009 10:37 PM 'Fluids' are a variety of things: smoke steam fire clouds rain poured liquids ocean waves river water waterfall mist/spray splashes lava ... A single type of solution can't cover them all! Intro - fluid types Fluids: Lagrangian, Eulerian techniques (13) file:///C:/stuff/content/misc/CS520/lectures/notes/lect_fluids/LagEuler.html#(1) 2 of 16 5/3/2009 10:37 PM We've already seen fluid animation techniques - particles-based, blobbies/level sets-based. They are 'arbitrary' (procedural). How about more formal techniques for fluid simulation? Two broad solution categories: Eulerian: fixed-space (grid-based) Lagrangian: free motion through space Intro - Eulerian, Lagrangian Fluids: Lagrangian, Eulerian techniques (13) file:///C:/stuff/content/misc/CS520/lectures/notes/lect_fluids/LagEuler.html#(1) 3 of 16 5/3/2009 10:37 PM Lagrangian: Navier-Stokes (N-S) equations are expressed in a 'material' (traveling) coordinate frame fluid flow is particles-based 'pressure' arises from inter-particle forces that seek to preserve density good for splashes, waterfalls etc. (where the fluid freely translates through space) downside - need LOTS of particles to obtain fluid *surfaces* Eulerian: N-S equations are expressed in a fixed, global frame hard to make the solution unconditionally stable good for 'contained' fluids (eg. in a cup, bathtub..) Lagrangian vs Eulerian Fluids: Lagrangian, Eulerian techniques (13) file:///C:/stuff/content/misc/CS520/lectures/notes/lect_fluids/LagEuler.html#(1) 4 of 16 5/3/2009 10:37 PM
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gradient (vector): given a scalar field f
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