This paper presents a non-reflecting boundary condition that significantly reduces the spurious pressure oscillations that are produced when vortical structures in a compressible flow cross the computational farfield boundaries. The method is based on commonly used characteristic boundary conditions. Here, incoming characteristics are ramped to zero in a buffer region as opposed to merely setting them to zero at the boundary. One of the key features of the approach is that it is free of coefficients requiring calibration. The equivalence of two formulations of the zonal boundary condition is verified with a model problem. Direct numerical simulations of trailing edges at different Mach numbers are conducted to demonstrate the effectiveness of the novel approach.