NUMERICAL VISCOSITIES OF DIFFERENCE-SCHEMES

Numerical visocisities 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 xi in a conventional Fourier stability analysis. A general formula is derived for the numerical viscosity in terms of the first and second derivatives of xi with respect to the wavenumber k, evaluate at k = 0. A single Fourier analysis therefore suffices to determine both stability limits and numerical viscosities.