To meet the milestones set by the High-Luminosity LHC (HL-LHC) project, the integration of new inner triplet magnet circuits is vital for enhancing the focusing of the particle beams at ATLAS and CMS. In addition to the Nb 3 Sn quadrupole magnets, high-order Nb-Ti magnets are required for field correction. This comprises self-protected magnets with six, eight, ten, and twelve poles, which also come in skewed variants. The simulation program LEDET was developed as part of the STEAM framework and is now applied to study quench transients in HL-LHC magnets. The electromagnetic and thermal transients occurring after a quench are simulated and validated with experiments at different current levels conducted by LASA (INFN). For the models, the three-dimensional geometry is accurately replicated and for each magnet the conductor parameters of each coil are set according to measurements. After discussing the various assumptions of the model, a simulation study is conducted to investigate the influence of the unknown quench location and inter-filament coupling losses. The developed models of each magnet show satisfactory accuracy and are predictive for different current levels. The models are then used to analyse the simulated hot-spot temperatures and peak voltages-to-ground, which cannot be easily measured. It is concluded that the protection strategy is effective.