Context. We report on new simultaneous observations and modeling of the millimeter, near-infrared, and X-ray flare emission of the source Sagittarius A* (SgrA*) associated with the super-massive (4 × 106 M⊙) black hole at the Galactic center. Aims. We study the applicability of the adiabatic synchrotron source expansion model and study physical processes giving rise to the variable emission of SgrA* from the radio to the X-ray domain. Methods. Our observations were carried out on 18 May 2009 using the NACO adaptive optics (AO) instrument at the European Southern Observatory’s Very Large Telescope, the ACIS-I instrument aboard the Chandra X-ray Observatory, the LABOCA bolometer at the Atacama Pathfinder EXperiment (APEX), and the CARMA mm telescope array at Cedar Flat, California. Results. The X-ray flare had an excess 2 − 8 keV luminosity between 6 and 12 × 1033 erg s-1. The observations reveal flaring activity in all wavelength bands that can be modeled as the signal from an adiabatically expanding synchrotron self-Compton (SSC) component. Modeling of the light curves shows that the sub-mm follows the NIR emission with a delay of about three-quarters of an hour with an expansion velocity of about vexp ~ 0.009c. We find source component sizes of around one Schwarzschild radius, flux densities of a few Janskys, and spectral indices α of about +1 (S(ν) ∝ ν−α). At the start of the flare, the spectra of the two main components peak just short of 1 THz. To statistically explain the observed variability of the (sub-)mm spectrum of SgrA*, we use a sample of simultaneous NIR/X-ray flare peaks and model the flares using a synchrotron and SSC mechanism. Conclusions. These parameters suggest that either the adiabatically expanding source components have a bulk motion larger than vexp or the expanding material contributes to a corona or disk, confined to the immediate surroundings of SgrA*. For the bulk of the synchrotron and SSC models, we find synchrotron turnover frequencies in the range of 300−400 GHz. For the pure synchrotron models, this results in densities of relativistic particles of the order of 106.5 cm-3 and for the SSC models, the median densities are about one order of magnitude higher. However, to obtain a realistic description of the frequency-dependent variability amplitude of SgrA*, models with higher turnover frequencies and even higher densities are required.