A solid fairing and a wire-mesh fairing consisting of very fine wires and pores are numerically and experimentally investigated for the mitigation of landing gear noise. A slightly modified LAGOON landing gear and two configurations, one equipped with a solid fairing and the other with a wire-mesh fairing, are numerically simulated using the Improved Delayed Detached-Eddy Simulation (IDDES) in combination with the Ffowcs Williams and Hawkings (FW-H) analogy. Instead of resolving the detailed flow features through the wire mesh, a recently proposed numerical model is used to represent the effect of the wire-mesh fairing. The simulated flow fields and the far-field noise spectra are validated against the experiments conducted in an anechoic wind tunnel. The superiority of the recently proposed wire-mesh model over a classical wire-mesh model in modelling both the aerodynamic and aeroacoustic effects of the wire mesh is demonstrated. Results also show that the dense wire-mesh fairing functions very similarly to the solid fairing and that significant noise can be reduced through the installation of a solid fairing or a wire-mesh fairing upstream of the landing gears. For the baseline landing gear, the torque link and the brakes are identified noise sources. With the aerodynamic penalty of a 50% increase in drag, both fairings mitigate the pressure fluctuation on the torque link and brakes, resulting in the reduction of surface noise sources. The noise directivity shows that a solid fairing or a dense wire-mesh fairing contributes to a noise reduction of 4-6 dB in all radial directions. The findings in this study pave the way for the low-noise design of aircraft landing gears.