Numerical Stability of Some Explicit FDMs for Variable Velocity Advection
by
John Noye
Department of Applied Mathematics, University of Adelaide
Coauthors: David McInerney (University of Adelaide)

The accurate modelling of advective terms in the equations of motion which govern fluid flow, and in the advection-diffusion equation which governs the spread of neutrally buoyant particles in a moving fluid, has been of interest to hydrologists, oceanographers and meteorologists for many years. The basis for their work has been the study of the one and two-dimensional advection equations, and a number of accurate high-order finite-difference methods (FDMs) for the constant velocity advection equation have been developed. Unfortunately, when used in the variable velocity case, these high-order methods generally degenerate at least one order.

In CTAC97, a technique for recovering the higher order of the constant coefficient FDM, when used in the variable coefficient case, was described. In this work, a number of explicit second-order FDMs for the variable velocity one-dimensional advection equation are described and their numerical stability is studied. Stability criteria obtained using the guidelines of Strikwerda and von Neumann are assessed by means of numerical experiments on these FDMs, particularly when the advective flow is oscillatory, which frequently occurs in coastal seas and estuaries.

Date received: July 29, 1999