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One more question about Jos Stam's GDC tutorial on stable fluids: in the advection step on page 8, the timestep for each dimension is implemented as dt * N, where N is the height or width of the grid. This corresponds to a position update:

$x_{prev} = x - \frac{\Delta t}{h} \cdot v_x$

where $h = 1/N$.

But why is $h$ involved in the backtracing of velocity? I thought the time evolution would just be given by $x = x_{prev} + \Delta t \cdot v_x$ without involving the grid size.

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Stam's code is written in such a way that the coordinates of the cell centers correspond to integers. This way, the cell where a particle ends can be easily determined by rounding (e.g. i0 = (int)x;) Likewise the starting point of backtracking is simply given by (i,j) (see e.g. x = i - dt0 * u[IX(i,j)]). So the computational problem is scaled such it makes computation simpler / easier to understand.

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  • $\begingroup$ Aha, of course. I forgot that the grid implicitly has unit length and height. $\endgroup$
    – jogloran
    Sep 27 '21 at 17:22

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