  2.5-dimensional magnetohydrodynamic (MHD) simulations are performed with high
spatial resolution in order to distinguish between competing models of the
coronal heating problem. A single coronal loop powered by Alfv\'{e}n waves
excited in the photosphere is the target of the present study. The coronal
structure is reproduced in our simulations as a natural consequence of the
transportation and dissipation of Alfv\'{e}n waves. Further, the coronal
structure is maintained as the spatial resolution is changed from 25 to 3 km,
although the temperature at the loop top increases with the spatial resolution.
The heating mechanisms change gradually across the magnetic canopy at a height
of 4 Mm. Below the magnetic canopy, both the shock and the MHD turbulence are
dominant heating processes. Above the magnetic canopy, the shock heating rate
reduces to less than 10 % of the total heating rate while the MHD turbulence
provides significant energy to balance the radiative cooling and thermal
conduction loss or gain. The importance of compressibility shown in the present
study would significantly impact on the prospects of successful MHD turbulence
theory in the solar chromosphere.
