A Stable and Accurate Numerical Method to Calculate the Motion of a Sharp Interface Between Fluids

Present address: Department of Applied Mathematics, University of Adelaide, G.P.O. Box 498, Adelaide, South Australia 5001. A spectrally accurate numerical method, which is also simpleto implement, is derived to calculate the motion of a fluidinterface. A numerical instability, typical of algorithms forthis problem, is investigated via a linearizing approximationwhich shows that a trivial adjustment of the algorithm rendersit numerically stable while retaining high accuracy. To testfor the correct implementation of the algorithm, non-linearsimultaneous equations are formulated using time derivativeinformation only from the coded procedure, whose solutions describeprogressive interfacial waves of permanent form. The behaviourof this type of algorithm when variations in the point spacingoccurs along the interface is investigated and found to cause"scattering" of travelling wave modes.