Numerical diffusion

Summary

Numerical diffusion is the smearing of a computed solution caused by the discretisation itself. It acts like an extra diffusion term that the original equation does not have. It is most visible in advection problems: a sharp front that should move without change of shape spreads out more and more. It is measured by the coefficient of the second-derivative term in the modified equation of the scheme. It is typical of first-order schemes such as the upwind scheme. Some numerical diffusion is often needed for stability, but too much of it destroys the resolution of fine features.