Abstract Large-eddy simulations with size-resolved microphysics are used to model persistent aircraft contrails and contrail-induced cirrus from a few wing spans behind the aircraft until their demise after many hours. Schemes for dynamic local ice binning and updating coupled radiation dynamically as needed in individual columns were developed for numerical efficiency, along with a scheme for maintaining realistic ambient turbulence over long times. These capabilities are used to study some of the critical dynamics involved in contrail evolution and to explore the simulation features required for adequate treatment of different components. A “quasi 3D” approach is identified as a useful approximation of the full dynamics, reducing the computation to allow a larger parameter space to be studied. Ice crystal number loss involving competition between different crystal sizes is found to be significant for both young contrails and aging contrail cirrus. As a consequence, the sensitivity to the initial number of ice crystals in the contrail above a threshold is found to decrease significantly over time, and uncertainties in the ice deposition coefficient and Kelvin effect for ice crystals assume an increased importance. Atmospheric turbulence is found to strongly influence contrail properties and lifetime in some regimes. Water from fuel consumption is found to significantly reduce aircraft-wake-induced ice crystal loss in colder contrails. Ice crystal shape effects, coupled radiation, and precipitation dynamics are also considered. An extensive set of simulations exploring a large parameter space with this model are analyzed in a companion paper.