The helicity injected torus with steady inductive helicity injection device is a simply-connected toroidal device that forms and sustains axisymmetric spheromak equilibria through the use of steady inductive helicity injection, which inject magnetic helicity through the inductive drive of non-axisymmetric currents on the edge of the plasma. Simulations of high-gain scenarios, using the NIMROD code and based on models validated with low gain experimental operations, indicate the formation of closed flux surfaces at current amplifications of six. Despite the helicity injection scheme adding magnetic perturbations of order , these closed flux equilibria are able to persist for as long as 20 injector periods (1.3 ms) before breaking apart due to other plasma generated instabilities.