Reference on a system of advection-diffusion-reaction equation in FEniCS Tutorial (Section 3.5)

mathematics
1

Hi All

This is a question about the FEniCS Tutorial book with title “Solving PDEs in Python–The FEniCS Tutorial Volume I” written by Hans Petter Langtangen and Anders Logg.

In section 3.5 of the FEniCS book, there is a three-equation system for modeling chemical reaction, advection and diffusion phenomena. Is this model built artificially for a demonstration of applying FEniCS to solve systems? Or, this model had been studied before and served as a well-accepted one in Chemistry? Could anyone kindly point to me some references for it, if the answer to my second question is yes.

Best wishes
Huadong

2

It derives from the standard continuum model conserving mass, momentum and energy. Its general formulation could be considered the compressible Navier-Stokes equations. Section 3.5 is a specialised case for three incompressible and miscible chemical species.

For an introduction consider the excellent book Bird Stewart & Lightfoot, Transport Phenomena.

3

Hi nate,

Thank you very much.
However that is a book with 928 pages : - )
I thought there will be some papers on this model.

4

It’s a very simple multicomponent mixture model. You’ll find it developed in introductory texts aimed at the undergraduate, or papers from the mid 19th Century.

5

Okay. From your reply, I got the truth: it is an old model and everything is clear about it. Thank you nate :smile:
Huadong