Quench Modeling in High-field Nb$_3$Sn Accelerator Magnets

The development of high-field magnets is on-going in the framework of the LHC luminosity upgrade. The resulting peak field, in the range of 12 T to 13 T, requires the use Nb$_{3}$Sn as superconductor. Due to the high stored energy density (compact winding for cost reduction) and the low stabilizer fraction (to achieve the desired margins), quench protection becomes a challenging problem. Accurate simulation of quench transientsin these magnets is hence crucial to the design choices, the definition of priority R&D; and to prove that the magnets are fit for operation. In this paper we focus on the modelling of quench initiation and propagation, we describe approaches that are suitable for magnet simulation, and we compare numerical results with available experimental data.