A high order finite difference scheme is introduced to deal with thermo-hydraulic quench simulation in superconducting magnets, specifically in the case of cable-in-conduit conductors (CICC). Liquid helium flow in CICC is governed by the unsteady convection-diffusion conservation equations, in the low Mach number and high Reynolds number flow, region. In the past. several years many methods have been considered for quench simulation in superconducting magnets, for example, finite element, finite volume, and finite difference methods. One of the main challenges is the accurate simulation of flow during a superconductor quench, given the large gradients in pressure and temperature that arise during conductor normalization. These simulations are key to proper magnet protection design. The Dispersion Relation Preserving (DRP) scheme is applied to the quench simulation problem. The computational results are,compared to those obtained using a well-proven commercial quench simulation code (Gandalf), as well as experimental data. Preliminary results are promising.