TRINITY: A coupled model of winds, radiation, and photoionised gas in molecular clouds. I. Methods and validation

Multi-wavelength surveys place cloud dispersal at 1-5 Myr after massive stars emerge, before the first supernovae. Whether a cloud disperses, re-collapses, or leaks Lyman-continuum (LyC) photons depends on how pre-supernova winds, radiation pressure, and photoionised-gas pressure (P HII) couple to the shell. We introduce TRINITY, a 1D thin-shell code that succeeds WARPFIELD. TRINITY evolves the bubble-shell structure under winds, supernovae, direct and dust-reprocessed radiation pressure, P HII, and gravity. A phase-aware prescription drives the shell with the larger of the hot-bubble and photoionised pressures when energy-driven, and P HII plus ram pressure when momentum-driven. The initial cloud may be uniform, a piecewise power law, or a Bonnor-Ebert sphere; shell structure, hot-bubble cooling, photon absorption, and LyC escape evolve with the dynamics. We validate against analytic wind and photoionisation limits and survey clouds of mass 10 5 - 10 6.5,M, core density 10 cubed - 10 4 cm-3, and star-formation efficiency epsilon=0.01 - 0.30. P HII enlarges the shell radius by roughly 17% at 10 Myr in the fiducial run. At higher efficiency, the energy-driven phase lasts under 1 Myr, radiation pressure stays sub-dominant, and P HII remains dynamically important in the momentum-driven phase. Cloud structure sets both phase durations and outcomes: at fixed mass, core density, and efficiency, homogeneous and shallow clouds re-collapse while a steep ρ proportional to r-2 cloud keeps expanding, and Bonnor-Ebert clouds disperse roughly 55% later than homogeneous ones. Thus P HII and cloud structure both shape feedback-driven expansion even when the stellar population is fixed. TRINITY is an efficient, interpretable framework to map feedback dominance across cloud parameter space and resolved H II regions.