## Jacob Bear Short Course – Day 1

As I mentioned before, I am currently attending a short course presented by Jacob Bear. The first day with ~6 hours of lecturing is over. These hours were some of the fastest lecturing hours I’ve experienced in my academic life to date. As I can tell so far, the advantages of such an experienced lecturer are:

- He has explained these things many times before, so he knows where he is coming from and where he’s going to;
- This experience is also clear in the way he explains things — he knows what to emphasize;

In terms of his lecturing style I like

1) that he stresses things clearly either by pointing them out directly or by repeating them. The repetition might be directly after the first time he mentions something, or the repetition might be some significant amount of time after the first mention;

2) the clearness how things evolve. At any point it is clear why we are discussing what we are discussing and where we are coming from. Mostly it is even clear where we are going to;

3) The way of his explanations. Usually the explanation evolves from a usually very basic question. How basic the questions are is sometimes startling. However, the answers to such seemingly simple questions provide quite a bit of insight:

- What is a porous medium?
- What is a continuum approach?
- What is a phase, what is a component?
- Why do we not solve “flow” with the Navier-Stokes equation? After all, we do know essentially everything at a macroscopic level!
- What is a model?
- What is a fluid?
*— The abstraction of “fluid” from “molecules” is a very nice comparison with the deduction of a REV!* - What is a water table?
*— If I learned one thing at Waterloo, I think I would choose this ðŸ™‚*

After these basic definitions, also including a discussion of modelling and the modelling process, we spent a lot of time of deriving the advection-dispersion equation, from two angles. – from a Darcy-angle and – from a momentum-equation angle.

The beautiful thing was how Jacob Bear showed, from first principles how the advection-dispersion equation is obtained under which assumptions. Again, this is nothing new, but new was at what basic level we started. Some of the averaging techniques Jacob Bear briefly showed us, and which were written down by Bear and Bachamat (1990), might deserve some deeper investigation. Also interesting is the concept to derive basic equations for any extensive quantity, add the above mentioned averaging rules, and substitute the desired quantity and you’re desired description is right there. Nice.

Tomorrow, we’ll be dealing with one of my current favourite topics, dispersion.