  We present an ab initio approach to the solar coronal heating problem by
modelling a small part of the solar corona in a computational box using a 3D
MHD code including realistic physics. The observed solar granular velocity
pattern and its amplitude and vorticity power spectra, as reproduced by a
weighted Voronoi tessellation method, are used as a boundary condition that
generates a Poynting flux in the presence of a magnetic field. The initial
magnetic field is a potential extrapolation of a SOHO/MDI high resolution
magnetogram, and a standard stratified atmosphere is used as a thermal initial
condition. Except for the chromospheric temperature structure, which is kept
fixed, the initial conditions are quickly forgotten because the included
Spitzer conductivity and radiative cooling function have typical timescales
much shorter than the time span of the simulation. After a short initial start
up period, the magnetic field is able to dissipate 3-4 10^6 ergs cm^{-2} s^{-1}
in a highly intermittent corona, maintaining an average temperature of $\sim
10^6$ K, at coronal density values for which emulated images of the Transition
Region And Coronal Explorer(TRACE) 171 and 195 pass bands reproduce observed
photon count rates.
