Subglacial drainage is a crucial component of the dynamics of glaciers and ice sheets, through its impact on basal sliding, ice flow velocities, and ultimately, glacier mass loss. Numerical models of subglacial drainage that combine both distributed and channelized flow in 2D have enabled many studies of subglacial hydrology and its link to ice flow. However, existing 2D models are fundamentally limited by their inability to incorporate the physical representation of ice uplift, when water pressure reaches ice overburden, and free-surface flow at atmospheric pressure. We present GlaDS-2, a new subglacial drainage model that addresses this modeling gap by incorporating bounded subglacial water pressures into a novel, unified, and mass-conserving formulation. GlaDS-2 builds upon the Glacier Drainage System (GlaDS) model by including physics-based representations of ice uplift and free-surface flow in addition to pressurized subglacial flow, and implicitly captures the evolving boundaries between different flow regimes.</p> <p>We showcase the new capabilities of the model by simulating a rapid supraglacial lake drainage on both synthetic and real topography from North Lake in Greenland. The model simulates the formation and dissipation of a traveling subglacial water blister inducing transient ice uplift, captures regions of free-surface flow at the ice margins, and integrates the modeling of proglacial flow dynamics. Our simulations demonstrate that the spatial and temporal extent of the ice uplift following the lake drainage is influenced by both englacial storage and the pre-existing state of the subglacial channel network. Overall, GlaDS-2 provides an improved numerical foundation for future coupled subglacial drainage and ice-flow modeling.