Page 150 - Process Modelling and Simulation With Finite Element Methods

Chapter 4

EXTENDED MULTIPHYSICS

W .B . J. ZIMMERMAN' , P.O.MCHEDLOV-PETROSSY AN2*
G.A. KHOMENK02
'Department of Chemical and Process Engineering, University of Sheffield, Newcastle
Street, Shefield SI 3JD United Kingdom; 'Labratoire d'Oceanografi,Cotiere du Littoral,
ELICO, Universite du Littoral Coted'Opale, MREN, 32, Avenue Foch, 62930,
Wimereux, France. *Permanent address: NSS Kharkov Institute of Physics and
Technology, Ukraine
E-mail: w.zimrnerman@she&ac.uk

Extended multiphysics is a feature that is conceptually complicated and original with
FEMLAB. The concept is the linkage of two or more logical computational domains
through coupling variables that can be used in either specifying the boundary conditions
or subdomain PDE coefficients. The coupling variables can be found by subdomain or
boundary integrations, internal or boundary values. These naturally arise in the multiple
scale modeling of physical phenomena - the large scale model is coupled to subgrid
cellular models, perhaps of a simpler parametric or lower spatial dimension. Extended
multiphysics is ubiquitous in process engineering, however, because unit operations are
conceptually separate domains, yet linked through at least inlet and exit conditions
sequentially, but frequently linked more subtly through process integration. So the whole
field of process simulation for optimization, design, retrofit, and control falls within the
remit of extended multiphysics. Integration with Simulink gives the possibility of some
unit operations being treated with distributed PDE models while others are treated with
lumped parameters, yet with non-trivial levels of coupling requiring extended
multiphysics modeling.

4.1 Introduction

If multiphysics, the subject of the last chapter, were a new concept to you,
extended multiphysics must be a more alien concept indeed. So far, I have seen
only one application of extended multiphysics - the Packed Bed Reactor model
in the Chemical Engineering ModuleModel library [ 11. Initially I thought
extended multiphysics was about coupling multiple scale models, as that is how
it was done in [I]. This is a cutting edge area of research in multiphase
flowsheterogeneous systems, because the dispersed phase can be treated as a
point constraint in the domain of the bulk medium, but with information flowing
in both directions. Usually the attempt is to treat such constraints parametrically,
i.e. modeling the dependence of the small scale phenomena on bulk phase
unknowns, and vice versa to complete the coupling of the scales. Usually, the
small scale phenomena is too complex in its own right, for instance in the

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