Numerical diffusion

Numerical diffusion is a difficulty with computer simulations of continuous systems such as fluids or plasmas. In Eulerian simulations, time and space are divided into a discrete grid and the continuous differential equations of motion (such as the Navier-Stokes equation are discretized into finite-difference equations. The discrete equations are in general more diffusive than the original differential equations, so that the simulated system behaves differently than the intended physical system. The amount and character of the difference depends on the system being simulated and the type of discretization that is used.

As an example of numerical diffusion, consider an Eulerian simulation of a drop of green dye diffusing through water. If the water is flowing diagonally through an Eulerian 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 transfer effect. 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.