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I'm a chemical engineering undergraduate and I'm currently starting to work in a theoretical transport phenomena/colloid science group.

While my group has a nice code base for larger scale simulations (by this I mean Monte Carlo/Molecular Dynamics/Brownian Dynamics type methods) it seems that when it comes to smaller problems that can be reduced to numerically solving pde's (with finite difference/elements methods for example) they tend to leave it to each student to learn by themselves.

Since I'm just starting out, I'd like to learn these methods well for future work.

Can anyone recommend a good book or reference for numerical methods in transport phenomena?

I'd prefer if it was focused on finite differences since that is the method I currently have the most familiarity with, but I'd be perfectly happy with any method.

Some extra notes: I am aware and have access to LeVeque's book, which I've seen mentioned as the standard introductory textbook. However I'd prefer something that is more focused on the specific needs and methods of transport phenomena.

I would be awesome if it was available for less than around $120 since that is what I have available right now, but I understand that might be unrealistic.

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Speaking as a chemical engineer, the numerical methods courses and textbooks I've seen come out of the field have been poor. There is the book by Beers, for instance, which was used as the main text when I studied for my PhD at MIT. The exposition isn't that great, and frankly, if you really get into any sort of numerical methods research, you'll be better served by having more depth in any of the topics covered in that book.

A cursory Amazon search pulled up Computational Transport Phenomena by Scheisser and Silebi. Scheisser is at Lehigh, and has long been a proponent of the method of lines, so you likely won't learn anything that isn't in LeVeque's book. The code samples look to be in Fortran 77, with bad practices like relying on IMPLICIT DOUBLE PRECISION, so you'll also pick up bad coding habits, too.

I'd recommend instead sticking with something like LeVeque or Strikwerda for finite difference methods, LeVeque or Toro for finite volume methods, or something like the text by Larson and Bengzon for finite element methods. I'd avoid recommending a text like Brenner and Scott to someone who doesn't have the pure math background, but it's a good book also. What discretization method you should use really depends on the problem; without more knowledge about the research problems you're interested in, I can't give you more specific recommendations.

Assuming you've got a good handle on transport phenomena at the level of a textbook like Bird, Stewart, and Lightfoot; Incropera and DeWitt; or Deen (which is fine for an advanced undergrad, but probably not my first choice, even though it's a great book), and you understand the numerical methods, you'll be in good shape, because frankly, you'll be better prepared than most of the grad students who come out of chemical engineering programs when it comes to numerical methods.

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  • $\begingroup$ Are there people that aren't "proponents of the method of lines"? It's such a broad term it seems every practical numerical method for time dependent PDEs uses it to the point it's never mentioned by name. $\endgroup$ – Aurelius Apr 23 '15 at 13:27
  • $\begingroup$ @Aurelius: Scheisser has published a lot of papers specifically about the method of lines, not merely about using the method of lines as one step in a derivation to obtain a semi-discretized collection of ODEs. I see what you're saying -- it's a very widely used numerical method -- and the distinction I'm drawing is that he chooses to focus his research on that one topic, whereas I think most people treat it as an established technology. $\endgroup$ – Geoff Oxberry Apr 23 '15 at 17:55

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