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To move in some direction (as a fluid does in a pipe). Often contrasted with diffusion, which is a spreading out without necessarily having any movement of the field as a whole.

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Finite volume piecewise linear 2D advection develops instability

A numerical scheme can be unconditionally unstable, conditionally stable and unconditionally stable. You would want the later two. I would recommend that you learn to do Von-Neumann stability ana …
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