Accurately predicting the formation, evolution, and breakdown of helicopter blade tip vortex is crucial for simulating the Blade-Vortex Interaction (BVI) phenomenon. Firstly, the high-order Perturbed polynomial reconstructed Targeted Essentially Non-Oscillatory (TENO-P) scheme proposed by our research group is employed to improve the resolution of the helicopter rotor flowfield solver. The TENO-P scheme, building on the fifth-order TENO5 scheme, achieves one-order of accuracy improvement by adaptively adjusting the values of the free-parameter introduced by perturbed polynomial reconstruction. Subsequently, the AH-1 helicopter model rotor undergoing blade-vortex interaction is analyzed using the improved rotor flowfield solver and the Farassat-1A formula. The implementation of the TENO-P scheme notably enhances the resolution of the rotor flowfield solver in resolving the blade tip vortex structures, and the predicted noise results are in good agreement with the experimental data. Finally, the alteration of the BVI noise and its reduction mechanism of the AH-1 model rotor under different Higher Harmonic Controls (HHC) are analyzed. The findings show that the phase modulation margin increases with a decrease in harmonic order, and the noise reduction effect significantly improves as well. The negative component of the higher harmonic control is beneficial for reducing BVI noise while the positive component of the higher harmonic control exacerbates the BVI noise. The HHC reduces the collective pitch angle in the region where the tip vortex is about to be disturbed, decreasing the strength of the blade tip vortex in this region. This reduction weakens the strength of the parallel and near-parallel interaction on the advancing side, leads to the reduction of the positive peak impulsive of the BVI noise, and consequently lowers the intensity of the BVI noise.