What is the meaning of the transportiveness property of a fluid flow and its relation with Peclet number ?

(1). I have never heard of such words as "transportiveness property of a fluid flow". Can you cite the source?

For fluid flow, transportiveness describes the influence on the upstream node on the downstream node.

For zero Peclet number (pure diffusion), the isolines of constant PHI (any field variable) around the node P are circular. The influence of PHI at P spreads equally (for constant diffusivity) in all directions.

For high Peclet numbers (assumed flow from the node P to E), PHI at P strongly influences the value of PHI at the downstream node E. But PHI at P is weakly influenced by PHI at E. The isolines of PHI at E are ellipses biased towards the upwind node P. The higher is the Peclet number the closer is the value of PHI at E to the value of PHI at P.

You should be able to see the transportive property in the numerical scheme. The coefficient matrix for a convection-diffusion problem will be unsymmetric. For the upwind node (P) the matrix coefficient (Ap-e) will include only diffusion. For the downstream node, convection and diffusion will be included in Ae-p. You can consult the description of the upwind schemes for the convection term for more information.

regards

DML

You will find some description on Transportiveness in: An introduction to Computational Fluid Dynamics: The finite Volume Method; HK Versteeg & W Malalasekera; 1995; Longman Scientific & Technical. Pages 7, 110, 112-114, 118, 123.

As I understand it, it is a term introduced to justify upwind differencing.