Thermophotonic devices are radiative heat engines in which the exchange of electroluminescent radiation between a heated light-emitting diode and a cool photovoltaic cell allows for the conversion of heat into electrical power. Here, we introduce CRESCENT-1D, the solver we have developed to simulate the performance of one-dimensional thermophotonic systems, which is made publicly available on GitHub. It couples photon transport in the far or near field, based on the fluctuational electrodynamics framework, and charge transport in heterostructures, modelled with the drift-diffusion and Poisson equations. We include both thermionic emission and charge carrier tunnelling to precisely model charge transport at heterointerfaces, while the photon chemical potential is computed in a self-consistent manner between the radiative and electrical sections of the solver. Compared to simpler formulations, these models provide accurate results at high voltages, which is essential to achieve high power output. The capabilities of CRESCENT-1D are illustrated with an optimised InGaP/InGaAs thermophotonic heterostructure, whose maximum power reaches 1.6 W.cm^{−2} for an efficiency of 19.7% considering a 300 K temperature difference between the light-emitting diode and the photovoltaic cell. This solver makes it possible for anyone to design various categories of optoelectronic structures (thermophotonics, light-emitting diode, thermophotovoltaics, thermoradiative, etc.), and represent an important step in the development of near-field radiative heat engines.