Page 16 - Process Modelling and Simulation With Finite Element Methods

Introduction to FEMLAB 3

Attitude

The attitude of this book is to demonstrate particular features of FEMLAB that
make computational modelling easy to implement, and then emphasize those
features that are advantages to modelling with FEMLAB. This will be illustrated
with reference to Chemical Engineering Modelling, which has a special history
and well known applications, The features, however, are generally applicable in
the sciences and engineering.

Bias
The book is slanted toward applications in fluid dynamics, transport phenomena,
and heterogeneous reaction, which reflect some of the research interests of the
author that routinely involve mathematical modelling by PDEs and solution by
numerical methods.

Modeling versus simulation
This book is about modelling and programming. The first four chapters, the core
of the taught module, focus completely on modeling. The remaining chapters
are slanted towards the use of FEMLAB for simulation. The distinction is that
simulation has some stochastic and evolutionary elements. Simulations may
have a PDE compute engine as an integral component, but generally involve
much more “user defined programming.” This book organizes case studies of
modeling along the lines of a cookbook - here are some models that are
important in chemical engineering applications that are computable in
MATLABEEMLAB. What is lacking from this presentation style, however, are
the philosophical and methodological aspects of modeling. This book is “How
To”, but not sufficiently “Why” and “How good?” are the models. There are
two major classes of modeling activity - (1) rigorous physicochemical modeling,
which takes the best understanding of physics and attempt to compute by
numerical methods the exact value up to the limits of finite precision
representation of numbers; (2) approximate modeling, which intends to
approximate the true, rigorous dynamics with simpler relationships in order to
estimate sizes of effects and features of the outcome, rather than exact, detailed
accuracy. In this book, no attempt is made to systematically treat how to
propose the equations and boundary conditions of modeling - decisions about
modeling objectives and acceptable approximations are presumed to have
already been taken rationally. Yet, in most modeling conundrums and trouble
shooting, whether or not the model itself is sensible is a key question, and what
level of approximation and inaccuracy are acceptable, are part and parcel of the
modeling activity. Numerics and scientificlengineering judgement about what
should be modelled and how should not be separated.