A novel numerical approach for simulating unstable nonlinear wavepackets in hypersonic boundary-layers is presented. The adaptive mesh refinement wavepacket tracking (AMR-WPT) method has been developed as an efficient alternative to conventional direct numerical simulations (DNS). The AMR-WPT method employs the nonlinear disturbances equations (NLDE), an overset dual mesh approach with higher-order interapolation, and adaptive mesh refinement (AMR) to track wavepackets in hypersonic boundary-layer flows. The AMR-WPT method is also extended for for complex geometries by coupling in an immersed boundary method (AMR-WPT-IBM). After introducing the numerical details, the method is employed to simulate linear and nonlinear wavepackets for an axisymmetric M=9.81 straight cone and 2-D/3-D M=5.35 flat plate boundary-layer. The simulation results are compared against classical stability and transition prediction tools, such as linear stability theory (LST), parabolized stability equations (PSE) and DNS. It is demonstrated that the AMR-WPT method requires only 10% of the number of grid points when compared to DNS of a nonlinear wavepacket inside a hypersonic flat plate boundary-layer flow.