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.
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