Page 120 - Process Modelling and Simulation With Finite Element Methods

Chapter 3

MULTIPHYSICS

W.B.J. ZIMMERMAN
Department of Chemical and Process Engineering, University of Sheffield,
Newcastle Street, Sheffield Sl 3JD United Kingdom

E-mail: w.zimmerman@shefiac.uk

Multiphysics is a recent conceptualization to categorize modeling where different
physicochemical mechanisms are prevalent in a given application, where these
mechanisms are modelled by wholly different field equations. But to be multiphysics,
the field equations must couple. In this chapter, we treat models of multiphysics for
thermoconvection and non-isothermal chemical reactors as examples of the genre of
multiphysics. Applications in later chapters show largely multiphysics modeling since
“single physics” models are likely to be well studied in their core disciplines. We also
take the opportunity to introduce the concept of parametric continuation, which is an
essential mechanism for arriving at the solution to highly nonlinear problems by inching
there by starting from nearby solutions in function space or even linear systems. The
model is then altered to treat the differential side wall heating of water between walls
held at the freezing and boiling points (without boiling) and the full dependency of
buoyant force on temperature. Simulations in large cavities show the beginnings of
stratification in temperature. Next we treat a non-isothermal tubular reactor that couples
mass and energy transport. Finally, we treat chemical reaction in the pores of a solid
pellet with diffusion from a bulk flow.

3.1 Introduction

FEMLAB makes a big selling point of multiphysics modelling as a key
advantage of its software package. Not long ago I described one of the
important features of the burgeoning research area of microfluidics as requiring
skills in multiphysics modelling. A respected colleague asked pointedly,
“What’s that? Physics that happens on multiple scales?” So multiphysics is
jargon that may not be uniformly recognized in the sciences and engineering.
Not wanting to use the term wildly, we shall define multiphysics modelling here
to mean any complete, coupled system of differential equations that has more
than one independent variable of different physical dimensions (vector equations
count as one equation). The FEMLAB definition is actually an operational
definition - “Does FEMLAB have a single application mode for it or can you
only describe it by coupling more than one application mode?” In FEMLAB’s
Model Navigator, you can create a multiphysics model by coupling two or more
application modes (under the multiphysics tab).

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