A jet attacking a edge oscillates spontaneously, and generates aerodynamic sound called edge tone. The edge tone is the sound source of air-jet instruments like a recorder and flute. The jet oscillation has several modes. While one of the modes is selected, the frequency increases linearly with the jet velocity. When the jet velocity exceeds a threshold, the mode transition arises, and it is hysteretic. The mode transition induces sudden changes of the frequency and the sound energy. Therefore, the reproducibility of the mode transition with a numerical calculation is crucial for understanding the mechanism of edge tone. In this study, the 2D model of edge tone is investigated with compressible DNS and LES. The DNS adopted in our study is an exact method without any artificial viscosity terms. The mode transition can be accurately reproduced with DNS. On the other hand, in some cases of calculations with LES, the mode transition cannot be reproduced even though the calculation is not broken down. We discuss the details of this problem.