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The Luminous Blue Variable stars exhibit behavior ranging from light curve`microvariations' on timescales of tens of days, to `outbursts' accompanied bymass loss of up to 10e-03 solar masses per year, occurring decades apart, to`giant eruptions' such as seen in Eta Carinae ejecting one or more solar massesand recurring on timescales of centuries. Here we review the work of the LosAlamos group since 1993 to investigate pulsations and instabilities in massivestars using linear pulsation models and non-linear hydrodynamic models. Themodels predict pulsational variability that may be associated with themicrovariations. Using a nonlinear pulsation hydrodynamics code with atime-dependent convection treatment, we show that, in some circumstances, theEddington limit is exceeded periodically in the pulsation driving region of thestellar envelope, accelerating the outer layers, and perhaps initiating massloss or LBV outbursts. We discuss how pulsations and mass loss may beresponsible for the location of the Humphreys-Davidson Limit in the H-Rdiagram. The `giant eruptions', however, must involve much deeper regions inthe stellar core to cause such large amounts of mass to be ejected. We reviewand suggest some possible explanations, including mixing from gravity modes,secular instabilities, the epsilon mechanism, or the SASI instability asproposed for Type II supernovae. We outline future work and required stellarmodeling capabilities to investigate these possibilities.

Pulsations and Hydrodynamics of Luminous Blue Variable Stars