Condensation trails (contrails) are increasingly recognized as a major contributor to aviation-induced atmospheric warming, rivaling the impact of carbon dioxide. Mitigating their climate effects requires accurate and computationally efficient models to inform avoidance strategies. Contrails evolve through distinct stages, from formation and rapid growth to dissipation or transition into cirrus clouds, where the latter phase critically determines their radiative forcing. This long-term evolution is primarily driven by advection-diffusion processes coupled with ice-particle growth dynamics. We propose a new multi-physics Eulerian framework for long-term contrail simulations, integrating underexplored or previously neglected factors, including spatiotemporal wind variability; nonlinear diffusion coefficients accounting for potential diffusion-blocking mechanisms; a novel multiphase theoretical model for the bulk settling velocity of ice particles; and ice-crystal habit dynamics. The Eulerian model is solved using a recently proposed discretization approach to enhance both accuracy and computational efficiency. Additionally, the Eulerian model introduces several theoretical, adjustable parameters that can be calibrated using ground-truth data to optimize the built-in nonlinear advection–diffusion equations (ADEs). We further demonstrate that the governing nonlinear ADEs admit dimensional separability under suitable assumptions, making the multi-physics Eulerian model particularly promising for large-scale simulations of contrail plumes and, ultimately, their associated radiative forcing.