Practical Investigation of Convective Difference Approximations of Reduced Dispersion

A survey of commonly used approximations to the Eulerian form of the equations of ideal fluid flow is given. Comparisons are made through amplitude and phase properties as determined by linear stability analysis. The unacceptable amplitude damping of first‐order approximations is reiterated. For second‐order approximations the discussion emphasizes numerical dispersion effects and shows that the familiar stable forms do not differ significantly in relative merit. Fourth‐order improvements are discussed with reference to further extensions which minimize dispersion. Conservative forms of the approximations are given along with experimentally determined properties regarding their nonlinear behavior in fluid‐dynamic calculations. Comments relating to fluid‐dynamic instability versus numerical instability are included.