A higher order numerical scheme for scalar transport

Abstract The computational principles of a numerical scheme for the solution of the two-dimensional scalar transport equation are presented. The scheme is designed for use in transient flow situations where accurate simulation of the advective process is important. Advective transport is computed by the method of characteristics in which the scalar field is represented by a Hermitian polynomial complete through the third degree in both coordinate directions, while diffusion is computed by central differencing. The superior accuracy of the new method is demonstrated by analysing its propagation characteristics and by comparing its performance on standard test problems with that of some well-known lower order methods. Finally, the method's applicability is demonstrated in several examples involving tracer releases into channel flows. Where possible the results of these simulations are compared with analytical solutions.