A novel nonreflecting boundary condition, which converges to the specified time-dependent boundary condition within any degree of accuracy, is introduced for the numerical simulation of hyperbolic systems and validated against the solution of two fundamental boundary value problems in fluids. First, transonic nozzle flow with backward acoustic disturbance is considered. Using high-order aeroacoustic numerical schemes, the proposed nonreflecting boundary condition yields results that are in excellent agreement with those obtained using conventional nonreflecting boundary conditions based on the method of characteristics as well as with the results of the exact solution. The novel nonreflecting boundary condition, implemented into a semi-analytical solution algorithm of unsteady bubbly cavitating nozzle flows, is also validated against results obtained using a Lagrangian finite volume scheme. Copyright (c) 2013 John Wiley & Sons, Ltd.