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tokens: by each successive refinement splitting a cell into two, and a refinement level of RL leads to cell sizes decreased by 1/2 RL . The maximum value of RL is taken as 13. This can lead to very small cells, with a commensurate decrease in the time step required for numerical stability. However individual loops can be simulated for reasonable real times (a few hours). Further details of the HYDRAD numerical method, including the finite difference schemes used, can be found in Appendix A.2 of BC13 and references therein. Such a “brute force” method is unlikely to be a viable way of running multi-dimensional codes. To this end we have developed an alternative approach, tested on one-dimensional problems ( Johnston et al. 2017a , b ), that treats the lower TR as an unresolved layer. By integrating the energy equation across this layer, and imposing a closure condition, we are able to provide rapid solutions to 1D problems with an accuracy that compares well with HYDRAD results. The details are found in Johnston et al. (2017a) , and we refer to this as the UTR method. It is incorporated into a one-dimensional version of the Lagrangian remap (Lare) code whose computational details are discussed in Arber et al. (2001) , referred to as “LareJ”. 2.2. Influence of numerical resolution We start by exploring the effect of numerical resolution on TNE cycles in coronal loop models. We model a coronal loop of total length 180 Mm with a small chromosphere attached to each end and select the largest grid cells in our calculations to have a width of 1 Mm. Thus, at the highest refinement level, the minimum cell width is 122 m. 2.2.1. Steady footpoint heating: HYDRAD simulations Representative of the conditions necessary to induce TNE in coronal loop models (e.g. Müller et al. 2003 ; Antolin et al. 2010 ; Peter et al. 2012 ; Mikić et al. 2013 ; Froment et al. 2018 ), we first consider the case of steady footpoint heating where the spatial profile is given by the sum of two Gaussian peaks (one at each loop leg), each defined as, These peaks are localised between the base of the corona and base of the TR with a maximal value at z = 12.5 Mm and we take z H = 1.5 Mm as the length scale of heat deposition. This is shown in Fig. 1 as the blue curve. We note that in this part of the paper a small spatially uniform background heating term is always present so that Q ( z ) = Q bg + Q H ( z ). This is commonly done in 1D loop models to ensure that T and n remain positive: here Q bg = 6.8682 × 10 −6 J m −3 s −1 and the effect of including a range of values of Q bg will be examined in Sect. 2.4 . Moreover, in order to avoid unrealistic pile up of condensations at the loop apex due to the symmetry of the model, the spatial symmetry of the heating profile is perturbed by adding a small enhancement of 0.4% to the Gaussian peak at the left-hand leg of the loop. The initial state of the loop is determined using just Q bg , leading to a temperature of order 1 MK. The footpoint