Context : We report on new modeling results based on the mm- to X-ray emission of the SgrA* counterpart associated with the massive \sim 4 \times 10 ^ { 6 } M _ { \odot } black hole at the Galactic Center . Aims : We investigate the physical processes responsible for the variable emission from SgrA* . Methods : Our modeling is based on simultaneous observations carried out on 07 July , 2004 , using the NACO adaptive optics ( AO ) instrument at the European Southern Observatory ’ s Very Large Telescope Based on observations at the Very Large Telescope ( VLT ) of the European Southern Observatory ( ESO ) on Paranal in Chile ; Program : 271.B-5019 ( A ) . and the ACIS-I instrument aboard the Chandra X-ray Observatory as well as the Submillimeter Array SMA The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics , and is funded by the Smithsonian Institution and the Academia Sinica . on Mauna Kea , Hawaii , and the Very Large Array The VLA is operated by the National Radio Astronomy Observatory which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities , Inc . in New Mexico . Results : The observations revealed several flare events in all wavelength domains . Here we show that the flare emission can be described with a combination of a synchrotron self-Compton ( SSC ) model followed by an adiabatic expansion of the source components . The SSC emission at NIR and X-ray wavelengths involves up-scattered sub-millimeter photons from a compact source component . At the start of the flare , spectra of these components peak at frequencies between several 100 GHz and 2 THz . The adiabatic expansion then accounts for the variable emission observed at sub-mm/mm wavelengths . The derived physical quantities that describe the flare emission give a blob expansion speed of v _ { exp } \sim 0.005 c , magnetic field of B around 60 G or less and spectral indices of \alpha =0.8 to 1.4 , corresponding to a particle spectral index p \sim 2.6 to 3.8 . Conclusions : A combined SSC and adiabatic expansion model can fully account for the observed flare flux densities and delay times covering the spectral range from the X-ray to the mm-radio domain . The derived model parameters suggest that the adiabatic expansion takes place in source components that have a bulk motion larger than v _ { exp } or the expanding material contributes to a corona or disk , confined to the immediate surroundings of SgrA* .