I'm trying to understand when and why one would use a staggered vs. a colocated grid in problems that have velocities and scalars that they transport (e.e. density).
If scalars are defined cell-centered, then in the physics world you often hear that velocities should be defined between cells, because apart from being intuitive, the resulting numerical schemes are stable.
I'm certain to having had heard this statement in the context of finite difference codes.
But now I'm learning finite volume methods with the Riemann Solvers by E. Toro. There, in the math world, vectors like velocities are just 3-scalars in equation systems that are all solved on one and the same colocated grid. There is never any mention of staggering grids at all (at least not as far as I got in the book, around Chapter 16, 3rd Ed.).
So is the choice of defining velocities on staggered vs. colocated grids related to the numerical methods one is using, or rather if one is solving ODEs vs. PDEs, or is the answer something completely different?