An Examination of Some Simple Numerical Schemes for Calculating Scalar Advection

Abstract

The computational damping and dispersion errors of some simple numerical schemes for calculating the advection of a scalar are analyzed. Computation times and accuracy are compared in calculating the two-dimensional transport of a symmetrical distribution in a uniform rotational flow field. Amplification factors, computational phase velocities and effective diffusion coefficients are used to examine the properties of the schemes. Simple tests show that the more accurate methods do not require significantly more computing times in both one and two-dimensional constant and variable flows. Among the better schemes, none can be singled out as ?best?. The cubic-spline and second-moment methods are particularly useful for regions of sharp concentration gradients or telescoping grids where the undamped, negative group velocities of the chapeau method prove troublesome. The ?best? scheme depends heavily on the geometry and physics of the problem.