  We present time dependent modeling based on the accretion disk limit cycle
model for a 270 d light curve of the short period SU UMa-type dwarf nova V344
Lyr taken by Kepler. The unprecedented precision and cadence (1 minute) far
surpass that generally available for long term light curves. The data encompass
two superoutbursts and 17 normal (i.e., short) outbursts. The main decay of the
superoutbursts is nearly perfectly exponential, decaying at a rate ~12 d/mag,
while the much more rapid decays of the normal outbursts exhibit a
faster-than-exponential shape. Our modeling using the basic accretion disk
limit cycle can produce the main features of the V344 Lyr light curve,
including the peak outburst brightness. Nevertheless there are obvious
deficiencies in our model light curves: (1) The rise times we calculate, both
for the normal and superoutbursts, are too fast. (2) The superoutbursts are too
short. (3) The shoulders on the rise to superoutburst have more structure than
the shoulder in the observed superoutburst and are too slow, comprising about a
third to half of the total viscous plateau, rather than the ~10% observed.
However, one of the alpha_{cold} -> alpha_{hot} interpolation schemes we
investigate (one that is physically motivated) does yield longer superoutbursts
with suitably short, less structured shoulders.
