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DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES

MASTER'S THESIS PRESENTATION

                    -Thursday, January 28, 19993

Simon Sivyer Clift, graduate student, Dept. Comp. Sci.,
Univ.  of Waterloo will speak on "Linear and Non-Linear
Methods    for    the    Incompressible   Navier-Stokes
Equations."

TIME:                4:00-5:00 p.m.

ROOM:                DC 1304

ABSTRACT

The  Navier-Stokes equations for incompressible viscous
fluid  flow  in  the  primitive variable form require a
great  deal  of computer time and storage for numerical
solution.   Recent studies have used Newton's method to
solve  the  discretized,  non-linear,  algebraic system
arising  from  these equations.  Either direct methods,
or iterative methods can be used to solve the resulting
linear   systems,   but  iterative  methods  have  been
demonstrated  to  be  faster and generally require less
storage.

A   two-stage   non-linear   method  using  the  slowly
converging,  but  robust ``frozen coefficient'' method,
and  full  Newton iteration, will be demonstrated to be
superior  to  the  use  of  either  method  alone.   An
iterative matrix solution based on CGSTAB acceleration,
and  a  preconditioner  based on the frozen coefficient
matrix   will  be  shown  to  be  efficient,  and  more
effective  than direct methods.  Issues of ordering and
preconditioning will be addressed, and it will be shown
that  completely  general  matrix  methods  can be used
efficiently.

Matrix  ordering, problem domain anisotropy, and finite
volume  cell  anisotropy will be shown to have profound
effects  on  the  efficiency of the solution method.  A
mixed   form  of  non-linear  iteration,  using  Newton
iteration  over  part of the problem domain, and frozen
coefficient iteration over the rest, will be outlined.

The  main  method  to be outlined solves incompressible
fluid  flow  to  arbitrary  precision,  and  has a time
                                                   3/2
complexity   measured  to  be  less  than  the  O(N   )

expected for an iterative method in two dimensions.

This presentation is being held in conjunction with the
Scientific Computation Group.