A Symmetric Total Variation Diminishing (STVD) scheme is applied to model the aeroacoustic and aerodynamics characteristics of rotors in hover. A modified version of the finite volume code TURNS (Transonic Unsteady Rotor Navier-Stokes) is used. The original TURNS solver uses a third order upwind scheme. The modified solver, referred to as TURNS-STVDx, is fourth, sixth, or eighth order accurate in space, and first or second order accurate in time. Calculations are presented for the high-speed impulsive noise emanating from a non-lifting UH-1H rotor, and the performance of the UH-60A rotor in hover. Encouraging improvements over the baseline method have been obtained. The modified method was not, however, able to model the tip vortex more accurately than the baseline solver. This is attributable to the numerical viscosity term that has the same form in the present solver and the baseline solver. Additional work is needed to improve the modeling of the tip vortex structure in the present methodology. In particular, higher order essentially nonoscillatory schemes (ENO) may be needed in the vicinity of the tip vortices.