Example
As an example of numerical diffusion, consider an Eulerian simulation using an explicit time-advance of a drop of green dye diffusing through water. If the water is flowing diagonally through the simulation grid, then it is impossible to move the dye in the exact direction of the flow: at each time step the simulation can at best transfer some dye in each of the vertical and horizontal directions. After a few time steps, the dye will have spread out through the grid due to this sideways transfer. This numerical effect takes the form of an extra high diffusion rate.
When numerical diffusion applies to the components of the momentum vector, it is called numerical viscosity; when it applies to a magnetic field, it is called numerical resistivity.
Read more about this topic: Numerical Diffusion
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