This paper is to investigate the flow non-linearity of the fluid-structural interaction using detached eddy simulation (DES) of turbulence. A low diffusion E-CUSP (LDE) scheme with 5th order WENO scheme is employed to calculate the inviscid fluxes. A fully conservative 4th order central differencing is used for the viscous terms. A fully coupled ffuid-structural model is employed. The limited cycle oscillation (LCO) of the NLR7301 airfoil is simulated in 2D using RANS method and in 3D using DES method. For the cases computed in this paper, the predicted LCO frequency, amplitudes, averaged lift and moment, all agree excellently with the experiment. The solutions appear to have bifurcation and are dependent on the initial fields or initial perturbation. The developed computational fluid dynamics (CFD)/computational structure dynamics (CSD) simulation is able to capture the LCO with very small amplitudes measured in the experiment. This is attributed to the high order low diffusion schemes, fully coupled FSI model, and the turbulence model used. This research appears to be the first time that a numerical simulation of LCO matches the experiment. The simulation confirms several observations of the experiment.