🚀 go-pugleaf

DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES

SCIENTIFIC COMPUTATION SEMINAR

                    -February 15, 1990  

Dr.  George  D.  Byrne, Exxon Research & Eng. Co.,
Annandale,  NJ  will  speak  on  ``The  Solution  of  a
Co-polymerization  Model with VODPK - Is That All There
Is?''

TIME:                 3:30 p.m.

ROOM:                 DC 1302

ABSTRACT

In this presentation, we describe the process of taking
a   chemical  engineering  problem,  working  with  the
engineer  to  develop  a reasonable mathematical model,
and  indicate  the process of developing a strategy for
solving  it.   The  strategy  includes  the  use  of  a
prototypical  software  package  (VODPK), with a backup
procedure.   The  objective  of this presentation is to
indicate  the  give  and  take  process of developing a
model,  developing  a  physical  feel  for  a  problem,
looking forward to an efficient computational solution,
and developing a bullet-proof code.

The clean-cut objective of the project is the numerical
solution  of a co-polymerization model by the numerical
method  of  lines  and  the  development  of a turn key
production  code.   The  mathematical  model is a mixed
system   of   partial  differential  equations  (PDEs),
algebraic  equations,  and  quadratures.   The PDEs are
also   of  mixed  type  -  parabolic,  hyperbolic,  and
elliptic.   With  the  algebraic  equations,  the  PDEs
describe  the  growth  of  polymers  within  a catalyst
pellet in the presence of two monomers.  The basic idea
is  that  the  monomers  join the polymer chains, which
grow and expand the spherical catalyst pellet.  Some of
the  reactions  occur  on a very fast time scale, while
others  are on a much slower time scale.  Consequently,
the pseudo-steady state assumption appears to be valid.
The   quadratures   are   used   to  calculate  several
parameters  that  are useful in the laboratory.  There,
actual   catalyst   pellets  are  dissected  and  their

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contents  analyzed  to  tune the several parameters for
the   manufacturing   process   and  further  numerical
simulation.   By the way, polymers are composed of long
molecular  chains  of  monomers  and  are  used to make
plastics and resins.

Computationally,  this is an interesting problem, since
we  are  calculating the solution of this system on the
interior  of  the  spherical  pellet, whose boundary is
moving outward as the polymerization process evolves in
time.  Moreover, much of the action is near this moving
boundary.   So  a  non-uniform grid is required for the
accurate   resolution   of  this  model.   To  conserve
computer  time  and storage, we plan to develop a black
box  preconditioner  and use it with a variant of GMRES
(SPIGMR)  in the prototypical ODE solver VODPK (written
by  Brown, Byrne, and Hindmarsh).  The backup procedure
involves the use of a band solver in VODE and a variant
of the orthonormalization process in SPIGMR (written by
Brown and Hindmarsh).