Identifying the heating mechanisms of the solar corona and the driving mechanisms of solar wind are key challenges in understanding solar physics. A full three-dimensional compressible magnetohydrodynamic (MHD) simulation was conducted to distinguish between the heating mechanisms in the fast solar wind above the open field region. Our simulation describes the evolution of the Alfv{e}nic waves, which includes the compressible effects from the photosphere to the heliospheric distance $s$ of 27 solar radii ($R_odot$). The hot corona and fast solar wind were reproduced simultaneously due to the dissipation of the Alfv{e}n waves. The inclusion of the transition region and lower atmosphere enabled us to derive the solar mass loss rate for the first time by performing a full three-dimensional compressible MHD simulation. The Alfv{e}n turbulence was determined to be the dominant heating mechanism in the solar wind acceleration region ($s>1.3 R_odot$), as suggested by previous solar wind models. In addition, shock formation and phase mixing are important below the lower transition region ($s<1.03R_odot$) as well.
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