  Coronal extreme-ultraviolet (EUV) waves are large-scale disturbances
propagating in the corona, whose physical nature and origin have been discussed
for decades. We report the first three dimensional (3D) radiative
magneto-hydrodynamic (RMHD) simulation of a coronal EUV wave and the
accompanying quasi-periodic wave trains. The numerical experiment is conducted
with the MURaM code and simulates the formation of solar active regions through
magnetic flux emergence from the convection zone to the corona. The coronal EUV
wave is driven by the eruption of a magnetic flux rope that also gives rise to
a C-class flare. It propagates in a semi-circular shape with an initial speed
ranging from about 550 to 700 km s$^{-1}$, which corresponds to an average Mach
number (relative to fast magnetoacoustic waves) of about 1.2. Furthermore, the
abrupt increase of the plasma density, pressure and tangential magnetic field
at the wavefront confirms fast-mode shock nature of the coronal EUV wave.
Quasi-periodic wave trains with a period of about 30 s are found as multiple
secondary wavefronts propagating behind the leading wavefront and ahead of the
erupting magnetic flux rope. We also note that the true wavefront in the 3D
space can be very inhomogeneous, however, the line-of-sight integration of EUV
emission significantly smoothes the sharp structures in 3D and leads to a more
diffuse wavefront.
