Numerical study of the stability of some explicit finite-difference methods for oscillatory advection

Abstract

The basis for modelling unsteady transport in fluids is the one-dimensional advection equation. When high-order finite-difference methods for constant velocity advection are applied to the variable velocity case, they generally degenerate at least one order. For example, Crowley's formula, which is second order for constant velocity advection, is only first order when used with variable velocities. Modification of Crowley's formula has recently yielded three formulae which are second order in the variable velocity case. Two commonly used local stability analyses have been carried out on these formulae with conflicting results. The resulting stability regions have been studied by means of a series of numerical experiments using an oscillatory advection velocity to determine their applicability in tidal streams.