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Advection of a Passive Scalar in One and Two Dimensions

UPDATED: 03/20/2018

This workbook is intended for use as demonstrations in an introductory course in Computational Fluid Dynamics and Heat Transfer at the 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. The five differencing schemes included are: simple upwind, weighted upwind, Quick (third order), Flux-corrected Transport (FCT) and Total Variation Diminishing (TVD).

Advection of a Passive Scalar in 1D – Comparison of five numerical schemes.

The second sheet demonstrates use of the upwind and weighted upwind schemes in two dimensions. A cone representing a passive scalar is advected for one orbit in a velocity field corresponding to solid body rotation. The resulting distribution is plotted at 22.5o degree intervals so as to give the illusion of animation.

Advection of a Passive Scalar in two dimensions. Comparison of two numerical schemes.

The numerical diffusion associated with the first-order method and dispersion associated with the second-order method are very evident.

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