Page 36 - Process Modelling and Simulation With Finite Element Methods

Chapter 1

FEMLAB AND THE BASICS OF NUMERICAL ANALYSIS

W.B.J. ZIMMEFWAN
Department of Chemical and Process Engineering, University of Sheffield,
Newcastle Street, Shefield SI 3JD United Kingdom

E-mail: w.zimrnerman @shejkc. uk

In this chapter, several key elements of numerical analysis are profiled in FEMLAB with
0-D and 1-D models. These elements are root finding, numerical integration by
marching, numerical integration of ordinary differential equations, and linear system
analysis. These methods underly nearly all problem solving techniques by numerical
analysis for chemical engineering applications. The use of these methods in FEMLAB is
illustrated with reference to some common applications in chemical engineering: flash
distillation, tubular reactor design, diffusive-reactive systems, and heat conduction in
solids.

1.1 Introduction
This chapter is rather busy, as it must accomplish several different goals.
Primarily, it is intended to introduce key features of how FEMLAB works.
Secondarily, it is to illustrate how these key features can be used to analyse
simple enough chemical engineering problems that 0-D and I-D spatial or
spatial-temporal systems can describe them. The chapter is also intended to
whet your interest to investigate modeling and simulation with FEMLAB by
presenting at least a glimpse of the power of the FEMLAB and MATLAB tools
when applied to chemical engineering analysis.
Because FEMLAB is not intended to be a general tool for problem solving,
some of these goals are achieved in a roundabout fashion. The author has
previously taught courses in chemical engineering problem solving by numerical
analysis using FORTRAN, MuthematicaTM, and MATLABTM, and used all the
examples implemented here with those tools. Furthermore, the most extensive
compilations of chemical engineering problem solving by numerical analysis
have been done in POLYMATH [l], which only seems to be used by the
chemical engineering community through the CACHE program.
The upshot is that for the examples in this chapter, FEMLAB is probably
not the package of first choice for the analysis. From the author’s experience
either MATLAB or Mathematica is preferable, with less overhead in setting up
the calculations. Nevertheless, even though FEMLAB was not necessarily
envisaged to solve such problems, that its numerical analysis tools are general

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