Physical and numerical dissipation and dispersion in viscous compressible flow computation

A general view is given of the roles of numerical dissipation and numerical dispersion in finite difference schemes for unsteady fluid dynamics and for unsteady magnetohydrodynamics, and of the problem of differentiating these numerical properties from the physical properties. These questions are studied by means of simple model equations, rather than in terms of the full set of Navier--Stokes or magnetohydrodynamic equations, but the ideas and results are generalizable to the full equations relatively directly. In the treatment of steady flows as long-time limits of time-dependent flows, it is found that a comparatively inaccurate time-dependent scheme may produce an accurate steady state, and vice versa. (3 figures) (U.S.)