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Say we have a lake of water and we drop a ball into a certain location of the water. Would it be efficient to use Eulerian for the water particles away from the ball drop and Lagrangian for water particles near it? Is this even plausible? Or is there another method that one would use?


How would we even track these qualities of all moving particles? Like any visible material in real world would consist of incredible many particles floating around, so any reasonably realistic simulation that uses movement of particles should also include similarly many particles, which is computationally almost impossible I presume?


What are some approaches we might use to find a good particle distribution? What is commonly done when using Lagrangian space discretization in practice-- selecting according to different distributions?


Are the Lagrangian particles like the particles from A4 (i.e. just a bunch of little balls / some other shape), or are they generally more abstract than that? If one were to simulate a pool of water as a ton of ball particles floating around, I feel like you would need a massive amount of extremely tiny particles to make it look like water and not like a ball pit. Could you instead treat the particles as, for example, points on a mesh that are connected to nearby points to make a more cohesive shape?


How would we assign grids for tracking velocity? Does each cell of the grid represent a particle? If yes, I think particles are moving, and how can we adjust grid assignment dynamically based on particles movement?


A more basic question: I'm having a hard time wrapping my head around how these two approaches relate to the actual PDE equation and all the variables involved, like u, u dot, u', etc. Could you elaborate on that?


I assume Eulerian discretization would be much easier to parallelize?


How fine does the Eulerian grid need to be? It seems as though motion might be very "low definition" so to speak if it is too coarse/ the squares are too large.


For Eulerian method, how is the resolution of the grid determined?


How are the number of particles for the Lagrangian method and the resolution of the grid for the Eulerian method decided?


Would Lagrangian incur greater overhead and be more costly to compute than Eulerian? In which cases or apps would we want to use one over the other?


In Eulerian, how can the velocity of a certain grid location be tracked?


Which of these two methods has better hardware efficiency?


It seems like the Lagrangian would take more computing power but would also lead to more realistic results. Is this true?


Is lagragian similar in concept to the idea of Brownian motion and particles suspended in space?


Are there other ways to discretize space or do other methods tend to build on these two?


For Eulerian, do we require less space because we're using grid positions instead of tracking all particles?


How much is the latency difference between the two methods?


Does the Eulerian take much less computing power in a scene with lots of particles since the variables that are stored are not dependent on the number of particles in the space?


I understand how the Eulerian method would be calculated by just checking the flux at fixed locations but for the Lagrangian method, how would we keep track of all the moving particles and would that ever be efficient as supposed to the fixed locations?