The design of the protection system for the superconducting elements in an accelerator such as the large Hadron collider (LHC), now under construction at CERN, requires a detailed understanding of the thermo-hydraulic and electrodynamic processes during a quench. A numerical program (SPQR ยฑ simulation program for quench research) has been developed to evaluate temperature and voltage distributions during a quench as a function of space and time. The quench process is simulated by approximating the heat balance equation with the ยฎnite dierence method in presence of variable cooling and powering conditions. The simulation predicts quench propagation along a superconducting cable, forced quenching with heaters, impact of eddy currents induced by a magnetic ยฎeld change, and heat transfer through an insulation layer into helium, an adjacent conductor or other material. The simulation studies allowed a better understanding of experimental quench data and were used for determining the adequate dimensioning and protection of the highly stabilised superconducting cables for connecting magnets (busbars), optimising the quench heater strip layout for the main magnets, and studying quench back by induced eddy currents in the superconductor. After the introduction of the theoretical approach, some applications of the simulation model for the LHC dipole and corrector magnets are presented and the outcome of the studies is compared with experimental data.