  We describe a new method for simulating ionizing radiation and supernova
feedback in the analogues of low-redshift galactic disks. In this method, which
we call star-forming molecular cloud (SFMC) particles, we use a ray-tracing
technique to solve the radiative transfer equation for ultraviolet photons
emitted by thousands of distinct particles on the fly. Joined with high
numerical resolution of 3.8 pc, the realistic description of stellar feedback
helps to self-regulate star formation. This new feedback scheme also enables us
to study the escape of ionizing photons from star-forming clumps and from a
galaxy, and to examine the evolving environment of star-forming gas clumps. By
simulating a galactic disk in a halo of 2.3e11 Msun, we find that the average
escape fraction from all radiating sources on the spiral arms (excluding the
central 2.5 kpc) fluctuates between 0.08% and 5.9% during a ~20 Myr period with
a mean value of 1.1%. The flux of escaped photons from these sources is not
strongly beamed, but manifests a large opening angle of more than 60 degree
from the galactic pole. Further, we investigate the escape fraction per SFMC
particle, f_esc(i), and how it evolves as the particle ages. We discover that
the average escape fraction f_esc is dominated by a small number of SFMC
particles with high f_esc(i). On average, the escape fraction from a SFMC
particle rises from 0.27% at its birth to 2.1% at the end of a particle
lifetime, 6 Myrs. This is because SFMC particles drift away from the dense gas
clumps in which they were born, and because the gas around the star-forming
clumps is dispersed by ionizing radiation and supernova feedback. The framework
established in this study brings deeper insight into the physics of photon
escape fraction from an individual star-forming clump, and from a galactic
disk.
