A
Comparison
of
Numerical
Methods
for
the
Rayleigh
Equation
in
Unbounded
Domains
(August 1991)Abstract
A
second-order
finite
difference
and
two
spectral
methods
including
a Cheby-
shev
tau
and
a Chebyshev
collocation
method
have
been
implemented
to
determine
the
linear
hydrodynamic
stability
of
an
unbounded
shear
flow.
The
velocity
profile
of
the
basic
flow
in
the
stability
analysis
mimicks
that
of
a
one-stream
free
mixillg
layer.
Local
and
global
eige\~value
solution
methods
are
used
to
determine
individ-
ual
ejgenvalues
and
the
eigenvalue
spectrum,
respectively.
The
calculated
eigen-
value
spectrum
includes
a discrete
mode,
a continuous
spectrum
associated
with
the
equation
singularity
and
a continuous
spectrum
associated
with
the
domain
unboundedness.
The
efficiency
and
the
accuracy
of
these
discretization
methods
in
the
prediction
of
the
eigensolutions
of
the
discrete
mode
have
been
evaluated
by
comparison
with
a conventional
shooting procedure.
Their
capabilities
in
mapping
out
the
continuous
eigenvalue
spectra
are
also
discussed.