Numerical viscosities of finite-difference schemes are usually obtained from truncation-error analyses based on Taylor series expansions. Here we observe that numerical viscosities can also be obtained very simply and directly from the growth factor ξ in a conventional Fourier stability analysis. A general formula is derived for the numerical viscosity in terms of the first and second derivatives of ξ with respect to the wavenumber k, evaluated at k = 0. A single Fourier analysis therefore suffices to determine both stability limits and numerical viscosities.

At the time of writing, John Ramshaw was affiliated with Idaho National Engineering Laboratory.