Advection of a Passive Scalar in One and Two Dimensions
This workbook is intended for use as demonstrations in an introductory course in Computational Fluid Dynamics and Heat Transfer at the introductory graduate and advanced undergraduate level. It consists of two sheets. On the first one the user can select one of five separate differencing schemes for the transient, one-dimensional advection equation and input the Courant number. Numerical diffusion and dispersion are vividly illustrated as the initially-square wave is advected across the plot. Differencing schemes included are simple upwind, weighted upwind, Quick (third order), Flux-corrected Transport (FCT) and Total Variation Diminishing (TVD).