We perform and analyze results of a global magnetohydrodyanmic (MHD) simulation of the fast coronal mass ejection (CME) that occurred on 2011 March 7. The simulation is made using the newly developed Alfven Wave Solar Model (AWSoM), which describes the background solar wind starting from the upper chromosphere and extends to 24 R$_{odot}$. Coupling AWSoM to an inner heliosphere (IH) model with the Space Weather Modeling Framework (SWMF) extends the total domain beyond the orbit of Earth. Physical processes included in the model are multi-species thermodynamics, electron heat conduction (both collisional and collisionless formulations), optically thin radiative cooling, and Alfven-wave turbulence that accelerates and heats the solar wind. The Alfven-wave description is physically self-consistent, including non-Wentzel-Kramers-Brillouin (WKB) reflection and physics-based apportioning of turbulent dissipative heating to both electrons and protons. Within this model, we initiate the CME by using the Gibson-Low (GL) analytical flux rope model and follow its evolution for days, in which time it propagates beyond STEREO A. A detailed comparison study is performed using remote as well as textit{in situ} observations. Although the flux rope structure is not compared directly due to lack of relevant ejecta observation at 1 AU in this event, our results show that the new model can reproduce many of the observed features near the Sun (e.g., CME-driven extreme ultraviolet (EUV) waves, deflection of the flux rope from the coronal hole, double-front in the white light images) and in the heliosphere (e.g., shock propagation direction, shock properties at STEREO A).
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