In this work, new methods are developed to facilitate stable and accurate numerical solutions of linearized Euler equations, which are often used in solving problems in com- putational aeroacoustics. Solutions of LEE can sufer from numerical Kelvin-Helmholtz instabilities in the presence of a sheared mean ow. Various methods have been exploited to address this problem; each has its advantages and disadvantages. In this work, two new methods that use artificial damping terms (ADT) are introduced. The first method is constructed to damp the vortical components generated during the computation while the second one is proposed by revisiting the effect of viscosity in the Navier-Stokes equations. An adaptive method is also used to improve the proposed new methods. These methods are tested on two benchmark cases: a) acoustic wave refraction through a strongly sheared jet, and b) mode radiation from a semi-infinite duct with jet. It is found that numeri- cal instabilities can be successfully suppressed with little side effect on the acoustic wave computations.